Generalizing normality for operators on Banach spaces: Hyponormality. I.
Vasile I. Istratescu (1983)
Collectanea Mathematica
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Vasile I. Istratescu (1983)
Collectanea Mathematica
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Miroslav Sova (1982)
Časopis pro pěstování matematiky
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K. Förster, E. Liebetrau (1977)
Studia Mathematica
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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.
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).
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.
Vladimír Lovicar (1975)
Časopis pro pěstování matematiky
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Earl Berkson, Ahmed Sourour (1974)
Studia Mathematica
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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.
Mecheri, Salah (2005)
Revista Colombiana de Matemáticas
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