Some uses of subharmonicity in functional analysis
Bernard Aupetit (1982)
Banach Center Publications
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Bernard Aupetit (1982)
Banach Center Publications
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N. Kalton (1995)
Studia Mathematica
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We construct a quasi-Banach space X which contains no basic sequence.
Nadia Boudi, Said Ouchrif (2009)
Studia Mathematica
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We study generalized derivations G defined on a complex Banach algebra A such that the spectrum σ(Gx) is finite for all x ∈ A. In particular, we show that if A is unital and semisimple, then G is inner and implemented by elements of the socle of A.
Camillo Trapani (2006)
Studia Mathematica
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A normal Banach quasi *-algebra (,) has a distinguished Banach *-algebra consisting of bounded elements of . The latter *-algebra is shown to coincide with the set of elements of having finite spectral radius. If the family () of bounded invariant positive sesquilinear forms on contains sufficiently many elements then the Banach *-algebra of bounded elements can be characterized via a C*-seminorm defined by the elements of ().
Heydar Radjavi, Peter Šemrl (2008)
Studia Mathematica
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Let X and Y be Banach spaces and ℬ(X) and ℬ(Y) the algebras of all bounded linear operators on X and Y, respectively. We say that A,B ∈ ℬ(X) quasi-commute if there exists a nonzero scalar ω such that AB = ωBA. We characterize bijective linear maps ϕ : ℬ(X) → ℬ(Y) preserving quasi-commutativity. In fact, such a characterization can be proved for much more general algebras. In the finite-dimensional case the same result can be obtained without the bijectivity assumption.
Elisabeth Werner (1988)
Mathematische Annalen
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Vladimír Müller (1988)
Studia Mathematica
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Burlando, Laura (1993)
International Journal of Mathematics and Mathematical Sciences
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Holger Rauhut (2007)
Colloquium Mathematicae
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We generalize the theory of Wiener amalgam spaces on locally compact groups to quasi-Banach spaces. As a main result we provide convolution relations for such spaces. Also we weaken the technical assumption that the global component is invariant under right translations, which is new even for the classical Banach space case. To illustrate our theory we discuss in detail an example on the ax+b group.
L. Waelbroeck (1982)
Banach Center Publications
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Fernando Albiac, José Ansorena (2012)
Open Mathematics
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Unlike for Banach spaces, the differentiability of functions between infinite-dimensional nonlocally convex spaces has not yet been properly studied or understood. In a paper published in this Journal in 2006, Bayoumi claimed to have discovered a new notion of derivative that was more suitable for all F-spaces including the locally convex ones with a wider potential in analysis and applied mathematics than the Fréchet derivative. The aim of this short note is to dispel this misconception,...
Vladimír Müller, Andrzej Sołtysiak (1989)
Studia Mathematica
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J. Achari (1976)
Matematički Vesnik
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