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### $〈2,1〉$-compact operators.

Sibirskij Matematicheskij Zhurnal

### $\left(r,p\right)$-absolutely summing operators on the space $C\left(T,X\right)$ and applications.

Abstract and Applied Analysis

### ${}^{\infty }$-vectors and boundedness

Annales Polonici Mathematici

The following two questions as well as their relationship are studied: (i) Is a closed linear operator in a Banach space bounded if its ${}^{\infty }$-vectors coincide with analytic (or semianalytic) ones? (ii) When are the domains of two successive powers of the operator in question equal? The affirmative answer to the first question is established in case of paranormal operators. All these investigations are illustrated in the context of weighted shifts.

### ${ℒ}_{\pi }$-Spaces and cone summing operators

Studia Mathematica

### 2-local Lie isomorphisms of operator algebras on Banach spaces

Studia Mathematica

Let X and Y be complex Banach spaces of dimension greater than 2. We show that every 2-local Lie isomorphism ϕ of B(X) onto B(Y) has the form ϕ = φ + τ, where φ is an isomorphism or the negative of an anti-isomorphism of B(X) onto B(Y), and τ is a homogeneous map from B(X) into ℂI vanishing on all finite sums of commutators.

### 2-summing multiplication operators

Studia Mathematica

Let 1 ≤ p < ∞, $={\left(Xₙ\right)}_{n\in ℕ}$ be a sequence of Banach spaces and ${l}_{p}\left(\right)$ the coresponding vector valued sequence space. Let $={\left(Xₙ\right)}_{n\in ℕ}$, $={\left(Yₙ\right)}_{n\in ℕ}$ be two sequences of Banach spaces, $={\left(Vₙ\right)}_{n\in ℕ}$, Vₙ: Xₙ → Yₙ, a sequence of bounded linear operators and 1 ≤ p,q < ∞. We define the multiplication operator ${M}_{}:{l}_{p}\left(\right)\to {l}_{q}\left(\right)$ by ${M}_{}\left({\left(xₙ\right)}_{n\in ℕ}\right):={\left(Vₙ\left(xₙ\right)\right)}_{n\in ℕ}$. We give necessary and sufficient conditions for ${M}_{}$ to be 2-summing when (p,q) is one of the couples (1,2), (2,1), (2,2), (1,1), (p,1), (p,2), (2,p), (1,p), (p,q); in the last case 1 < p < 2, 1 < q < ∞.

### A Berezin-type map and a class of weighted composition operators

Concrete Operators

In this paper we consider the map L defined on the Bergman space [...] of the right half plane [...] .

### A Borel extension approach to weakly compact operators on ${C}_{0}\left(T\right)$

Czechoslovak Mathematical Journal

Let $X$ be a quasicomplete locally convex Hausdorff space. Let $T$ be a locally compact Hausdorff space and let ${C}_{0}\left(T\right)=\left\{f\phantom{\rule{0.222222em}{0ex}}T\to I$, $f$ is continuous and vanishes at infinity$\right\}$ be endowed with the supremum norm. Starting with the Borel extension theorem for $X$-valued $\sigma$-additive Baire measures on $T$, an alternative proof is given to obtain all the characterizations given in  for a continuous linear map $u\phantom{\rule{0.222222em}{0ex}}{C}_{0}\left(T\right)\to X$ to be weakly compact.

### A ${C}^{*}$-algebraic Schoenberg theorem

Annales de l'institut Fourier

Let $𝔄$ be a ${C}^{*}$-algebra, $G$ a compact abelian group, $\tau$ an action of $G$ by $*$-automorphisms of $𝔄,{𝔄}^{\tau }$ the fixed point algebra of $\tau$ and ${𝔄}_{F}$ the dense sub-algebra of $G$-finite elements in $𝔄$. Further let $H$ be a linear operator from ${𝔄}_{F}$ into $𝔄$ which commutes with $\tau$ and vanishes on ${𝔄}^{\tau }$. We prove that $H$ is a complete dissipation if and only if $H$ is closable and its closure generates a ${C}_{0}$-semigroup of completely positive contractions. These complete dissipations are classified in terms of certain twisted negative definite...

### A canonical trace associated with certain spectral triples.

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

### A characterisation of dilation-analytic operators

Annales de l'I.H.P. Physique théorique

### A characterization for the spectral capacity of a finite system of operators

Czechoslovak Mathematical Journal

### A characterization of chaotic order and a problem.

Journal of Inequalities and Applications [electronic only]

### A characterization of commutators with Hilbert transforms

Studia Mathematica

### A characterization of formally symmetric unbounded operators.

Publications de l'Institut Mathématique. Nouvelle Série

### A Characterization of Matrix Operators on l2.

Mathematische Zeitschrift

### A characterization of polynomially Riesz strongly continuous semigroups

Commentationes Mathematicae Universitatis Carolinae

In this paper we characterize the class of polynomially Riesz strongly continuous semigroups on a Banach space $X$. Our main results assert, in particular, that the generators of such semigroups are either polynomially Riesz (then bounded) or there exist two closed infinite dimensional invariant subspaces ${X}_{0}$ and ${X}_{1}$ of $X$ with $X={X}_{0}\oplus {X}_{1}$ such that the part of the generator in ${X}_{0}$ is unbounded with resolvent of Riesz type while its part in ${X}_{1}$ is a polynomially Riesz operator.

### A Characterization of Riesz Operators.

Mathematische Zeitschrift

### A Characterization of Schwartz Spaces.

Mathematische Zeitschrift

### A characterization of spectral operators of finite type

Compositio Mathematica

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