Titlebook: Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation; 22nd International W Manuel Cepedello Boiso,Håkan He

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Additive Maps Preserving the Inner Local Spectral Radius,Let . be a complex Banach space and let . be the algebra of all bounded linear operators on .. We characterize additive continuous maps from . onto itself which preserve the inner local spectral radius at a nonzero fixed vector.

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Weighted Composition Operators from the Analytic Besov Spaces to BMOA,Let . and . be analytic functions on the open unit disk . with .. We characterize the bounded and the compact weighted composition operators . from the analytic Besov space . . into . and into .. We also show that there are no isometries among the composition operators.

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,-algebras Generated by Truncated Toeplitz Operators,We obtain an analogue of Coburn’s description of the Toeplitz algebra in the setting of truncated Toeplitz operators. As a byproduct, we provide several examples of complex symmetric operators which are not unitarily equivalent to truncated Toeplitz operators having continuous symbols.

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On Some Vector Differential Operators of Infinite Order,In the paper some classes of vector differential operators of infinite order are studied and their use for constructing the entire solutions of implicit linear differential equations in a Banach space is considered. In addition, the integral representations of the Cauchy type for vector differential operators of infinite order are obtained.

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Tauberian Operators. Properties, Applications and Open Problems,Tauberian operators have been useful in the study of many different topics of functional analysis. Here we describe some properties and the main applications of tauberian operators, and we point out several concrete problems that remain open.

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The Cauchy Singular Integral Operator on Weighted Variable Lebesgue Spaces,Let .: ℝ → (1,∞) be a globally log-Hölder continuous variable exponent and .: ℝ →[0,∞] be a weight. We prove that the Cauchy singular integral operator . is bounded on the weighted variable Lebesgue space . .(ℝ,.)= {.:. .ϵ. .(ℝ)} if and only if the weight . satisfies..

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,Extension of Certain Distributions onWeighted Hölder Space and the Riemann Boundary Value Problem fLet Γ be a non-rectifiable curve on the complex plane ℂ. We extend distributional derivative . . of a function ., which is holomorphic in domain . Γ, up to continuous functional on the weighted Hölder space and apply this extension for solution of the Riemann boundary value problem on the curve Γ.

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Non-negative Self-adjoint Extensions in Rigged Hilbert Space,structed by means of the adjoint operator Å. (bi-extensions). Criteria of existence and descriptions of such extensions and associated closed forms are obtained. Moreover, we introduce the concept of an extremal nonnegative bi-extension and provide its complete description. After that we state and p