Mostrando recursos 1 - 20 de 404

  1. On some Hardy-type inequalities for fractional calculus operators

    Iqbal, Sajid; Pečarić, Josip; Samraiz, Muhammad; Tomovski, Zivorad
    In this article we present applications of Hardy-type and refined Hardy-type inequalities for a generalized fractional integral operator involving the Mittag-Leffler function in its kernel and for the Hilfer fractional derivative using convex and monotone convex functions.

  2. Additive maps preserving Drazin invertible operators of index $n$

    Mbekhta, Mostafa; Oudghiri, Mourad; Souilah, Khalid
    Given an integer $n\geq2$ , in this article we provide a complete description of all additive surjective maps on the algebra of all bounded linear operators acting on an infinite-dimensional complex Banach space, preserving in both directions the set of Drazin invertible operators of index $n$ .

  3. Lattice properties of the core-partial order

    Djikić, Marko S.
    We show that in an arbitrary Hilbert space, the set of group-invertible operators with respect to the core-partial order has the complete lower semilattice structure, meaning that an arbitrary family of operators possesses the core-infimum. We also give a necessary and sufficient condition for the existence of the core-supremum of an arbitrary family, and we study the properties of these lattice operations on pairs of operators.

  4. On a generalized Šemrl’s theorem for weak 2-local derivations on $B(H)$

    Cabello, Juan Carlos; Peralta, Antonio M.
    We prove that, for every complex Hilbert space $H$ , every weak 2-local derivation on $B(H)$ or on $K(H)$ is a linear derivation. We also establish that every weak 2-local derivation on an atomic von Neumann algebra or on a compact C $^{*}$ -algebra is a linear derivation.

  5. Radon–Nikodym theorems for operator-valued measures and continuous generalized frames

    Li, Fengjie; Li, Pengtong
    In this article we determine that an operator-valued measure (OVM) for Banach spaces is actually a weak∗ measure, and then we show that an OVM can be represented as an operator-valued function if and only if it has $\sigma$ -finite variation. By the means of direct integrals of Hilbert spaces, we introduce and investigate continuous generalized frames (continuous operator-valued frames, or simply CG frames) for general Hilbert spaces. It is shown that there exists an intrinsic connection between CG frames and positive OVMs. As a byproduct, we show that a Riesz-type CG frame does not exist unless the associated measure...

  6. New results on Kottman’s constant

    Castillo, Jesús M. F.; González, Manuel; Papini, Pier Luigi
    We present new results on Kottman’s constant of a Banach space, showing (i) that every Banach space is isometric to a hyperplane of a Banach space having Kottman’s constant 2 and (ii) that Kottman’s constant of a Banach space and of its bidual can be different. We say that a Banach space is a Diestel space if the infimum of Kottman’s constants of its subspaces is greater that 1. We show that every Banach space contains a Diestel subspace and that minimal Banach spaces are Diestel spaces.

  7. Norm estimates for random polynomials on the scale of Orlicz spaces

    Defant, Andreas; Mastyło, Mieczysław
    We prove an upper bound for the supremum norm of homogeneous Bernoulli polynomials on the unit ball of finite-dimensional complex Banach spaces. This result is inspired by the famous Kahane–Salem–Zygmund inequality and its recent extensions; in contrast to the known results, our estimates are on the scale of Orlicz spaces instead of $\ell_{p}$ -spaces. Applications are given to multidimensional Bohr radii for holomorphic functions in several complex variables, and to the study of unconditionality of spaces of homogenous polynomials in Banach spaces.

  8. Composition operators on the Bloch space of the unit ball of a Hilbert space

    Blasco, Oscar; Galindo, Pablo; Lindström, Mikael; Miralles, Alejandro
    Every analytic self-map of the unit ball of a Hilbert space induces a bounded composition operator on the space of Bloch functions. Necessary and sufficient conditions for compactness of such composition operators are provided, as well as some examples that clarify the connections among such conditions.

  9. The approximate hyperplane series property and related properties

    Acosta, María D.; Aron, Richard Martin; García-Pacheco, Francisco Javier
    We show that the approximate hyperplane series property consequence, we obtain that the class of spaces $Y$ such that the pair $(\ell_{1},Y)$ has the Bishop–Phelps–Bollobás property for operators is stable under finite $\ell_{p}$ -sums for $1\leq p\lt \infty$ . We also deduce that every Banach space of dimension at least $2$ can be equivalently renormed to have the AHSp but to fail Lindenstrauss’ property $\beta$ . We also show that every infinite-dimensional Banach space admitting an equivalent strictly convex norm also admits such an equivalent norm failing the AHSp.

  10. On cohomology for product systems

    Hong, Jeong Hee; Son, Mi Jung; Szymański, Wojciech
    A cohomology for product systems of Hilbert bimodules is defined via the $\operatorname{Ext}$ functor. For the class of product systems corresponding to irreversible algebraic dynamics, relevant resolutions are found explicitly and it is shown how the underlying product system can be twisted by 2-cocycles. In particular, this process gives rise to cohomological deformations of the $C^{*}$ -algebras associated with the product system. Concrete examples of deformations of the Cuntz’s algebra ${\mathcal{Q}}_{\mathbb{N}}$ arising this way are investigated, and we show that they are simple and purely infinite.

  11. Extended spectrum and extended eigenspaces of quasinormal operators

    Cassier, Gilles; Alkanjo, Hasan
    We say that a complex number $\lambda$ is an extended eigenvalue of a bounded linear operator $T$ on a Hilbert space $\mathcal{H}$ if there exists a nonzero bounded linear operator $X$ acting on $\mathcal{H}$ , called the extended eigenvector associated to $\lambda$ , and satisfying the equation $TX=\lambda XT$ . In this article, we describe the sets of extended eigenvalues and extended eigenvectors for the quasinormal operators.

  12. Ergodic behaviors of the regular operator means

    Suciu, Laurian
    This article deals with some ergodic properties for general sequences in the closed convex hull of the orbit of some (not necessarily power-bounded) operators in Banach spaces. A regularity condition more general than that of ergodicity is used to obtain some versions of the Esterle–Katznelson–Tzafriri theorem. Also, the ergodicity of the backward iterates of a sequence is proved under appropriate assumptions as, for example, its peripheral boundedness on the unit circle. The applications concern uniformly Kreiss-bounded operators, and other ergodic results are obtained for the binomial means and some operator means related to the Cesàro means.

  13. Triangular summability and Lebesgue points of $2$ -dimensional Fourier transforms

    Weisz, Ferenc
    We consider the triangular $\theta$ -summability of $2$ -dimensional Fourier transforms. Under some conditions on $\theta$ , we show that the triangular $\theta$ -means of a function $f$ belonging to the Wiener amalgam space $W(L_{1},\ell_{\infty})({\mathbb{R}}^{2})$ converge to $f$ at each modified strong Lebesgue point. The same holds for a weaker version of Lebesgue points for the so-called modified Lebesgue points of $f\in W(L_{p},\ell_{\infty})({\mathbb{R}}^{2})$ whenever $1\lt p\lt \infty$ . Some special cases of the $\theta$ -summation are considered, such as the Weierstrass, Abel, Picard, Bessel, Fejér, de La Vallée-Poussin, Rogosinski, and Riesz summations.

  14. Order structure, multipliers, and Gelfand representation of vector-valued function algebras

    Arhippainen, Jorma; Kauppi, Jukka; Mattas, Jussi
    We continue the study begun by the third author of $C^{*}$ -Segal algebra-valued function algebras with an emphasis on the order structure. Our main result is a characterization theorem for $C^{*}$ -Segal algebra-valued function algebras with an order unitization. As an intermediate step, we establish a function algebraic description of the multiplier module of arbitrary Segal algebra-valued function algebras. We also consider the Gelfand representation of these algebras in the commutative case.

  15. $\ell_{p}$ -maximal regularity for a class of fractional difference equations on UMD spaces: The case $1\lt \alpha\leq2$

    Lizama, Carlos; Murillo-Arcila, Marina
    By using Blunck’s operator-valued Fourier multiplier theorem, we completely characterize the existence and uniqueness of solutions in Lebesgue sequence spaces for a discrete version of the Cauchy problem with fractional order $1\lt \alpha\leq2$ . This characterization is given solely in spectral terms on the data of the problem, whenever the underlying Banach space belongs to the UMD-class.

  16. Unbounded composition operators via inductive limits: Cosubnormal operators with matrix symbols, II

    Budzyński, Piotr; Dymek, Piotr; Płaneta, Artur
    This article deals with unbounded composition operators with infinite matrix symbols acting in $L^{2}$ -spaces with respect to the Gaussian measure on $\mathbb{R}^{\infty}$ . We introduce weak cohyponormality classes $\mathcal{S}_{n,r}^{*}$ of unbounded operators and provide criteria for the aforementioned composition operators to belong to $\mathcal{S}_{n,r}^{*}$ . Our approach is based on inductive limits of operators.

  17. Approximative compactness in Musielak–Orlicz function spaces of Bochner type

    Shang, Shaoqiang; Cui, Yunan
    In this article, we give the criteria for approximative compactness of every proximinal convex subset of Musielak–Orlicz–Bochner function spaces equipped with the Orlicz norm. As a corollary, we give the criteria for approximative compactness of Musielak–Orlicz–Bochner function spaces equipped with the Orlicz norm.

  18. Hlawka’s functional inequality on topological groups

    Fechner, Włodzimierz
    Let $(X,+)$ be a topological abelian group. We discuss regularity of solutions $f\colon X\to\mathbb{R}$ of Hlawka’s functional inequality ¶ \[f(x+y)+f(y+z)+f(x+z)\leq f(x+y+z)+f(x)+f(y)+f(z),\] postulated for all $x,y,z\in X$ . We study the lower and upper hull of $f$ . Moreover, we provide conditions which imply continuity of $f$ . We prove, in particular, that if $X$ is generated by any neighborhood of zero, $f$ is continuous at zero, and $f(0)=0$ , then $f$ is continuous on $X$ .

  19. Duality for ideals of Lipschitz maps

    Cabrera-Padilla, M. G.; Chávez-Domínguez, J. A.; Jiménez-Vargas, A.; Villegas-Vallecillos, Moisés
    We develop a systematic approach to the study of ideals of Lipschitz maps from a metric space to a Banach space, inspired by classical theory on using Lipschitz tensor products to relate ideals of operator/tensor norms for Banach spaces. We study spaces of Lipschitz maps from a metric space to a dual Banach space that can be represented canonically as the dual of a Lipschitz tensor product endowed with a Lipschitz cross-norm, and we show that several known examples of ideals of Lipschitz maps (Lipschitz maps, Lipschitz $p$ -summing maps, maps admitting Lipschitz factorization through subsets of $L_{p}$ -space) admit...

  20. Spaceability in norm-attaining sets

    Falcó, Javier; García, Domingo; Maestre, Manuel; Rueda, Pilar
    We study the existence of infinite-dimensional vector spaces in the sets of norm-attaining operators, multilinear forms, and polynomials. Our main result is that, for every set of permutations $P$ of the set $\{1,\ldots,n\}$ , there exists a closed infinite-dimensional Banach subspace of the space of $n$ -linear forms on $\ell_{1}$ such that, for all nonzero elements $B$ of such a subspace, the Arens extension associated to the permutation $\sigma$ of $B$ is norm-attaining if and only if $\sigma$ is an element of $P$ . We also study the structure of the set of norm-attaining $n$ -linear forms on $c_{0}$ .

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