Mostrando recursos 1 - 20 de 315

  1. Local Lie derivations on certain operator algebras

    Liu, Dan; Zhang, Jianhua
    In this paper, we investigate local Lie derivations of a certain class of operator algebras and show that, under certain conditions, every local Lie derivation of such an algebra is a Lie derivation.

  2. Hadamard gap series in weighted-type spaces on the unit ball

    Hu, Bingyang; Li, Songxiao
    We give a sufficient and necessary condition for an analytic function $f(z)$ on the unit ball $\mathbb{B}$ in $\mathbb{C}^{n}$ with Hadamard gaps, that is, for $f(z)=\sum_{k=1}^{\infty}P_{n_{k}}(z)$ where $P_{n_{k}}(z)$ is a homogeneous polynomial of degree $n_{k}$ and $n_{k+1}/n_{k}\ge c\gt 1$ for all $k\in\mathbb{N}$ , to belong to the weighted-type space $H^{\infty}_{\mu}$ and the corresponding little weighted-type space $H^{\infty}_{\mu,0}$ under some condition posed on the weighted funtion $\mu$ . We also study the growth rate of those functions in $H^{\infty}_{\mu}$ .

  3. Triple solutions for quasilinear one-dimensional $p$ -Laplacian elliptic equations in the whole space

    Bonanno, Gabriele; O’Regan, Donal; Vetro, Francesca
    In this paper, we establish the existence of three possibly nontrivial solutions for a Dirichlet problem on the real line without assuming on the nonlinearity asymptotic conditions at infinity. As a particular case, when the nonlinearity is superlinear at zero and sublinear at infinity, the existence of two nontrivial solutions is obtained. This approach is based on variational methods and, more precisely, a critical points theorem, which assumes a more general condition than the classical Palais–Smale condition, is exploited.

  4. Some operator inequalities for unitarily invariant norms

    Zhao, Jianguo; Wu, Junliang
    This note aims to present some operator inequalities for unitarily invariant norms. First, a Zhan-type inequality for unitarily invariant norms is given. Moreover, some operator inequalities for the Cauchy–Schwarz type are also established.

  5. $L^{p}$ -Inequalities and Parseval-type relations for the Mehler–Fock transform of general order

    González, Benito J.; Negrín, Emilio R.
    In this article we study new $L^{p}$ -boundedness properties for the Mehler–Fock transform of general order on the spaces $L^{p}((0,\infty),e^{\alpha x}dx)$ and $L^{p}((0,\infty),(1+x)^{\gamma}dx)$ , $1\leq p\leq\infty$ , and $\alpha,\gamma\in\mathbb{R}$ . We also obtain Parseval-type relations over these spaces.

  6. Geometric constants of $\pi/2$ -rotation invariant norms on $\mathbb{R}^{2}$

    Tomizawa, Yukino; Mitani, Ken-Ichi; Saito, Kichi-Suke; Tanaka, Ryotaro
    In this article, we study the (modified) von Neumann–Jordan constant and Zbăganu constant of $\pi/2$ -rotation invariant norms on $\mathbb{R}^{2}$ . Some estimations of these geometric constants are given. As an application, we construct various examples consisting of $\pi/2$ -rotation invariant norms.

  7. Nonsimplicity of certain universal ${\mathrm{C}}^{\ast}$ -algebras

    de Jeu, Marcel; El Harti, Rachid; Pinto, Paulo R.
    Given $n\geq2$ , $z_{ij}\in\mathbb{T}$ such that $z_{ij}=\overline{z}_{ji}$ for $1\leq i,j\leq n$ and $z_{ii}=1$ for $1\leq i\leq n$ , and integers $p_{1},\ldots,p_{n}\geq1$ , we show that the universal ${\mathrm{C}}^{\ast}$ -algebra generated by unitaries $u_{1},\ldots,u_{n}$ such that $u_{i}^{p_{i}}u_{j}^{p_{j}}=z_{ij}u_{j}^{p_{j}}u_{i}^{p_{i}}$ for $1\leq i,j\leq n$ is not simple if at least one exponent $p_{i}$ is at least two. We indicate how the method of proof by “working with various quotients” can be used to establish nonsimplicity of universal ${\mathrm{C}}^{\ast}$ -algebras in other cases.

  8. Weighted backward shift operators with invariant distributionally scrambled subsets

    Wu, Xinxing; Wang, Lidong; Chen, Guanrong
    We obtain a sufficient condition to ensure that weighted backward shift operators on Köthe sequence spaces $\lambda_{p}(A)$ admit an invariant distributionally $\varepsilon$ -scrambled subset for any $0\lt \varepsilon\lt \operatorname{diam}\lambda_{p}(A)$ . In particular, every Devaney chaotic weighted backward shift operator on $\lambda_{p}(A)$ supports such a subset.

  9. A note on Weyl-type theorems and restrictions

    Chen, Lihong; Su, Weigang
    Let $X$ be a Banach space, let $T\in L(X)$ be a bounded linear operator, and let $T_{n}$ be a restriction of $T$ on $R(T^{n})$ . This article should be viewed as a note on the research work of Carpintero et al. We give here several different proofs for completeness, and we show the relations of $T$ and $T_{n}$ to a much greater extent. Moreover, we give sufficient conditions for which Weyl-type theorems for $T$ are equivalent to Weyl-type theorems for $T_{n}$ .

  10. Generalized shift-invariant systems and approximately dual frames

    Benavente, Ana; Christensen, Ole; Zakowicz, María I.
    Dual pairs of frames yield a procedure for obtaining perfect reconstruction of elements in the underlying Hilbert space in terms of superpositions of the frame elements. However, practical constraints often force us to apply sequences that do not exactly form dual frames. In this article, we consider the important case of generalized shift-invariant systems and provide various ways of estimating the deviation from perfect reconstruction that occur when the systems do not form dual frames. The deviation from being dual frames will be measured either in terms of a perturbation condition or in terms of the deviation from equality in...

  11. Perspectives and completely positive maps

    Hansen, Frank
    We study the filtering of the perspective of a regular operator map of several variables through a completely positive linear map. By this method we are able to extend known operator inequalities of two variables to several variables, with applications in the theory of operator means of several variables. We also extend Lieb and Ruskai’s convexity theorem from two to $n+1$ operator variables for any natural number $n$ .

  12. Computation of Riemann matrices for the hyperbolic curves of determinantal polynomials

    Chien, Mao-Ting; Nakazato, Hiroshi
    The numerical range of a matrix, according to Kippenhahn, is determined by a hyperbolic determinantal form of linear Hermitian matrices associated to the matrix. On the other hand, using Riemann theta functions, Helton and Vinnikov confirmed that a hyperbolic form always admits a determinantal representation of linear real symmetric matrices. The Riemann matrix of the hyperbolic curve plays the main role in the existence of real symmetric matrices. In this article, we implement computations of the Riemann matrix and the Abel–Jacobi variety of the hyperbolic curve associated to a determinantal polynomial of a matrix. Further, we prove that the lattice...

  13. An Inequality for expectation of means of positive random variables

    Gibilisco, Paolo; Hansen, Frank
    Suppose that $X$ , $Y$ are positive random variables and $m$ is a numerical (commutative) mean. We prove that the inequality $\mathrm{E}(m(X,Y))\leqm(\mathrm{E}(X),\mathrm{E}(Y))$ holds if and only if the mean is generated by a concave function. With due changes we also prove that the same inequality holds for all operator means in the Kubo–Ando setting. The case of the harmonic mean was proved by C. R. Rao and B. L. S. Prakasa Rao.

  14. Hyperrigid operator systems and Hilbert modules

    Shankar, P.; Vijayarajan, A. K.
    It is shown that, for an operator algebra $A$ , the operator system $S=A+A^{*}$ in the $C^{*}$ -algebra $C^{*}(S)$ , and any representation $\rho$ of $C^{*}(S)$ on a Hilbert space $\mathcal{H}$ , the restriction $\rho_{|_{S}}$ has a unique extension property if and only if the Hilbert module $\mathcal{H}$ over $A$ is both orthogonally projective and orthogonally injective. As a corollary we deduce that, when $S$ is separable, the hyperrigidity of $S$ is equivalent to the Hilbert modules over $A$ being both orthogonally projective and orthogonally injective.

  15. A Grüss type operator inequality

    Bottazzi, T.; Conde, C.
    In 2001, Renaud obtained a Grüss type operator inequality involving the usual trace functional. In this article, we give a refinement of that result, and we answer positively Renaud’s open problem.

  16. Baskakov–Szász-type operators based on inverse Pólya–Eggenberger distribution

    Kajla, Arun; Acu, Ana Maria; Agrawal, P. N.
    The present article deals with the modified forms of the Baskakov and Szász basis functions. We introduce a Durrmeyer-type operator having the basis functions in summation and integration due to Stancu (1970) and Pǎltǎnea (2008). We obtain some approximation results, which include the Voronovskaja-type asymptotic formula, local approximation, error estimation in terms of the modulus of continuity, and weighted approximation. Also, the rate of convergence for functions with derivatives of bounded variation is established. Furthermore, the convergence of these operators to certain functions is shown by illustrative graphics using MAPLE algorithms.

  17. The generalized Drazin inverse of the sum in a Banach algebra

    Mosić, Dijana; Zou, Honglin; Chen, Jianlong
    In this article, we obtain new additive results on the generalized Drazin inverse of a sum of two elements in a Banach algebra. Applying these additive results, we also give explicit formulas for the generalized Drazin inverse of a block matrix in a Banach algebra.

  18. $\varphi$ -contractibility and character contractibility of Fréchet algebras

    Abtahi, Fatemeh; Rahnama, Somaye
    Right $\varphi$ -contractibility and right character contractibility of Banach algebras have been introduced and investigated. Here, we introduce and generalize these concepts for Fréchet algebras. We then verify available results about right $\varphi$ -contractibility and right character contractibility of Banach algebras for Fréchet algebras. Moreover, we provide related results about Segal–Fréchet algebras.

  19. Similarity orbits of complex symmetric operators

    Zhu, Sen; Zhao, Jiayin
    An operator $T$ on a complex Hilbert space $\mathcal{H}$ is said to be complex symmetric if $T$ can be represented as a symmetric matrix relative to some orthonormal basis for $\mathcal{H}$ . In this article we explore the stability of complex symmetry under the condition of similarity. It is proved that the similarity orbit of an operator $T$ is included in the class of complex symmetric operators if and only if $T$ is an algebraic operator of degree at most $2$ .

  20. Geometric description of multiplier modules for Hilbert $C^{*}$ -modules in simple cases

    Jingming, Zhu
    In this article we suggest a vector bundle description for multiplier modules of vector bundles over noncompact spaces. We prove that the isomorphism classes of multiplier modules are dependent on the isomorphism classes of their underlying modules. This gives a way to evaluate the set of extensions of Hilbert modules in topological terms in simple cases.

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