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On the Banach-Stone problem

Jyh-Shyang Jeang, Ngai-Ching Wong (2003)

Studia Mathematica

Let X and Y be locally compact Hausdorff spaces, let E and F be Banach spaces, and let T be a linear isometry from C₀(X,E) into C₀(Y,F). We provide three new answers to the Banach-Stone problem: (1) T can always be written as a generalized weighted composition operator if and only if F is strictly convex; (2) if T is onto then T can be written as a weighted composition operator in a weak sense; and (3) if T is onto and F does not contain a copy of ℓ ₂ ∞ then T can be written as a weighted composition...

On the ℒ -characteristic of fractional powers of linear operators

Jürgen Appell, Marilda A. Simões, Petr P. Zabrejko (1994)

Commentationes Mathematicae Universitatis Carolinae

We describe the geometric structure of the ℒ -characteristic of fractional powers of bounded or compact linear operators over domains with arbitrary measure. The description builds essentially on the Riesz-Thorin and Marcinkiewicz-Stein-Weiss- Ovchinnikov interpolation theorems, as well as on the Krasnosel’skij-Krejn factorization theorem.

On the space of φ-nuclear operators on l2.

Marilda A. Simoes (1990)

Collectanea Mathematica

We consider the generalization Sphi of the Schatten classes Sp obtained in correspondence with opportune continuous, strictly increasing, sub-additive functions phi such that phi(0) = 0 and phi(1) = 1. The purpose of this note is to study the spaces Sphi of the phi-nuclear operators and to compare their properties to those of the by now well-known space S1 of nuclear operators.

On the spectral multiplicity of a direct sum of operators

M. T. Karaev (2006)

Colloquium Mathematicae

We calculate the spectral multiplicity of the direct sum T⊕ A of a weighted shift operator T on a Banach space Y which is continuously embedded in l p and a suitable bounded linear operator A on a Banach space X.

On totally * -paranormal operators

Eungil Ko, Hae-Won Nam, Young Oh Yang (2006)

Czechoslovak Mathematical Journal

In this paper we study some properties of a totally * -paranormal operator (defined below) on Hilbert space. In particular, we characterize a totally * -paranormal operator. Also we show that Weyl’s theorem and the spectral mapping theorem hold for totally * -paranormal operators through the local spectral theory. Finally, we show that every totally * -paranormal operator satisfies an analogue of the single valued extension property for W 2 ( D , H ) and some of totally * -paranormal operators have scalar extensions....

On truncations of Hankel and Toeplitz operators.

Aline Bonami, Joaquim Bruna (1999)

Publicacions Matemàtiques

We study the boundedness properties of truncation operators acting on bounded Hankel (or Toeplitz) infinite matrices. A relation with the Lacey-Thiele theorem on the bilinear Hilbert transform is established. We also study the behaviour of the truncation operators when restricted to Hankel matrices in the Schatten classes.

On Volterra composition operators from Bergman-type space to Bloch-type space

Zhi Jie Jiang (2011)

Czechoslovak Mathematical Journal

Let ϕ be an analytic self-mapping of 𝔻 and g an analytic function on 𝔻 . In this paper we characterize the bounded and compact Volterra composition operators from the Bergman-type space to the Bloch-type space. We also obtain an asymptotical expression of the essential norm of these operators in terms of the symbols g and ϕ .

Opening gaps in the spectrum of strictly ergodic Schrödinger operators

Artur Avila, Jairo Bochi, David Damanik (2012)

Journal of the European Mathematical Society

We consider Schrödinger operators with dynamically defined potentials arising from continuous sampling along orbits of strictly ergodic transformations. The Gap Labeling Theorem states that the possible gaps in the spectrum can be canonically labelled by an at most countable set defined purely in terms of the dynamics. Which labels actually appear depends on the choice of the sampling function; the missing labels are said to correspond to collapsed gaps. Here we show that for any collapsed gap,...

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