Displaying similar documents to “Power factorization in Banach modules over commutative radical Banach algebras.”

On Cohen's proof of the Factorization Theorem

Jan Kisyński (2000)

Annales Polonici Mathematici

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Various proofs of the Factorization Theorem for representations of Banach algebras are compared with its original proof due to P. Cohen.

Quasicompact endomorphisms of commutative semiprime Banach algebras

Joel F. Feinstein, Herbert Kamowitz (2010)

Banach Center Publications

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This paper is a continuation of our study of compact, power compact, Riesz, and quasicompact endomorphisms of commutative Banach algebras. Previously it has been shown that if B is a unital commutative semisimple Banach algebra with connected character space, and T is a unital endomorphism of B, then T is quasicompact if and only if the operators Tⁿ converge in operator norm to a rank-one unital endomorphism of B. In this note the discussion is extended in two ways: we discuss endomorphisms...

Character contractibility of Banach algebras and homological properties of Banach modules

Rasoul Nasr-Isfahani, Sima Soltani Renani (2011)

Studia Mathematica

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Let 𝓐 be a Banach algebra and let ϕ be a nonzero character on 𝓐. We give some necessary and sufficient conditions for the left ϕ-contractibility of 𝓐 as well as several hereditary properties. We also study relations between homological properties of some Banach left 𝓐-modules, the left ϕ-contractibility and the right ϕ-amenability of 𝓐. Finally, we characterize the left character contractibility of various Banach algebras related to locally compact groups.

Range inclusion results for derivations on noncommutative Banach algebras

Volker Runde (1993)

Studia Mathematica

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Let A be a Banach algebra, and let D : A → A be a (possibly unbounded) derivation. We are interested in two problems concerning the range of D: 1. When does D map into the (Jacobson) radical of A? 2. If [a,Da] = 0 for some a ∈ A, is Da necessarily quasinilpotent? We prove that derivations satisfying certain polynomial identities map into the radical. As an application, we show that if [a,[a,[a,Da]]] lies in the prime radical of A for all a ∈ A, then D maps into the radical. This generalizes...

On the uniqueness of uniform norms and C*-norms

P. A. Dabhi, H. V. Dedania (2009)

Studia Mathematica

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We prove that a semisimple, commutative Banach algebra has either exactly one uniform norm or infinitely many uniform norms; this answers a question asked by S. J. Bhatt and H. V. Dedania [Studia Math. 160 (2004)]. A similar result is proved for C*-norms on *-semisimple, commutative Banach *-algebras. These properties are preserved if the identity is adjoined. We also show that a commutative Beurling *-algebra L¹(G,ω) has exactly one uniform norm if and only if it has exactly one C*-norm;...

Polynomially compact derivations on Banach algebras

Matej Brešar, Yuri V. Turovskii (2009)

Studia Mathematica

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We consider a continuous derivation D on a Banach algebra 𝓐 such that p(D) is a compact operator for some polynomial p. It is shown that either 𝓐 has a nonzero finite-dimensional ideal not contained in the radical rad(𝓐) of 𝓐 or there exists another polynomial p̃ such that p̃(D) maps 𝓐 into rad(𝓐). A special case where Dⁿ is compact is discussed in greater detail.