Displaying similar documents to “Commuting C 0 groups and the Fuglede-Putnam theorem”

The inclusion theorem for multiple summing operators

David Pérez-García (2004)

Studia Mathematica

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We prove that, for 1 ≤ p ≤ q < 2, each multiple p-summing multilinear operator between Banach spaces is also q-summing. We also give an improvement of this result for an image space of cotype 2. As a consequence, we obtain a characterization of Hilbert-Schmidt multilinear operators similar to the linear one given by A. Pełczyński in 1967. We also give a multilinear generalization of Grothendieck's Theorem for GT spaces.

Narrow operators and rich subspaces of Banach spaces with the Daugavet property

Vladimir M. Kadets, Roman V. Shvidkoy, Dirk Werner (2001)

Studia Mathematica

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Let X be a Banach space. We introduce a formal approach which seems to be useful in the study of those properties of operators on X which depend only on the norms of the images of elements. This approach is applied to the Daugavet equation for norms of operators; in particular we develop a general theory of narrow operators and rich subspaces of spaces X with the Daugavet property previously studied in the context of the classical spaces C(K) and L₁(μ).

Exponentials of normal operators and commutativity of operators: a new approach

Mohammed Hichem Mortad (2011)

Colloquium Mathematicae

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We present a new approach to the question of when the commutativity of operator exponentials implies that of the operators. This is proved in the setting of bounded normal operators on a complex Hilbert space. The proofs are based on some results on similarities by Berberian and Embry as well as the celebrated Fuglede theorem.

Composition of (E,2)-summing operators

Andreas Defant, Mieczysław Mastyło (2003)

Studia Mathematica

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The Banach operator ideal of (q,2)-summing operators plays a fundamental role within the theory of s-number and eigenvalue distribution of Riesz operators in Banach spaces. A key result in this context is a composition formula for such operators due to H. König, J. R. Retherford and N. Tomczak-Jaegermann. Based on abstract interpolation theory, we prove a variant of this result for (E,2)-summing operators, E a symmetric Banach sequence space.