Recursos de colección
Project Euclid (Hosted at Cornell University Library) (191.996 recursos)
Annals of Functional Analysis
Annals of Functional Analysis
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.
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 $H^{\infty}_{\mu}$ .
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.
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.
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.
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.
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.
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.
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 $T_{n}$ .
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...
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 $n$ .
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...
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.
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.
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.
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.
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.
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.
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 $2$ .
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.