On some classes of BCH-algebras.
Chaudhry, Muhammad Anwar, Fakhar-Ud-Din, Hafiz (2001)
International Journal of Mathematics and Mathematical Sciences
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Chaudhry, Muhammad Anwar, Fakhar-Ud-Din, Hafiz (2001)
International Journal of Mathematics and Mathematical Sciences
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Rafał Bocian, Andrzej Skowroński (2016)
Colloquium Mathematicae
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We complete the derived equivalence classification of all weakly symmetric algebras of domestic type over an algebraically closed field, by solving the problem of distinguishing standard and nonstandard algebras up to stable equivalence, and hence derived equivalence. As a consequence, a complete stable equivalence classification of weakly symmetric algebras of domestic type is obtained.
Wong, Pak-Ken (1994)
International Journal of Mathematics and Mathematical Sciences
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J.D. Maitland Wright (1980)
Mathematische Zeitschrift
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J. Alaminos, R. Payá, A. R. Villena (2003)
Studia Mathematica
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We give a sufficient condition on a C*-algebra to ensure that every weakly compact operator into an arbitrary Banach space can be approximated by norm attaining operators and that every continuous bilinear form can be approximated by norm attaining bilinear forms. Moreover we prove that the class of C*-algebras satisfying this condition includes the group C*-algebras of compact groups.
Walden Freedman (1997)
Studia Mathematica
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An alternative to the Dunford-Pettis Property, called the DP1-property, is introduced. Its relationship to the Dunford-Pettis Property and other related properties is examined. It is shown that -direct sums of spaces with DP1 have DP1 if 1 ≤ p < ∞. It is also shown that for preduals of von Neumann algebras, DP1 is strictly weaker than the Dunford-Pettis Property, while for von Neumann algebras, the two properties are equivalent.
H. Garth Dales, Shital R. Patel, Charles J. Read (2010)
Banach Center Publications
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We consider Fréchet algebras which are subalgebras of the algebra 𝔉 = ℂ [[X]] of formal power series in one variable and of 𝔉ₙ = ℂ [[X₁,..., Xₙ]] of formal power series in n variables, where n ∈ ℕ. In each case, these algebras are taken with the topology of coordinatewise convergence. We begin with some basic definitions about Fréchet algebras, (F)-algebras, and other topological algebras, and recall some of their properties; we discuss Michael's problem from 1952 on the continuity...
Scott Saccone (1995)
Studia Mathematica
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We use the work of J. Bourgain to show that some uniform algebras of analytic functions have certain Banach space properties. If X is a Banach space, we say X is strongif X and X* have the Dunford-Pettis property, X has the Pełczyński property, and X* is weakly sequentially complete. Bourgain has shown that the ball-algebras and the polydisk-algebras are strong Banach spaces. Using Bourgain’s methods, Cima and Timoney have shown that if K is a compact planar set and A is R(K) or A(K),...
Halaš, R., Plojhar, L. (2005)
International Journal of Mathematics and Mathematical Sciences
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M. A. Chebotar, W.-F. Ke, P.-H. Lee, N.-C. Wong (2003)
Studia Mathematica
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Let θ : ℳ → 𝓝 be a zero-product preserving linear map between algebras. We show that under some mild conditions θ is a product of a central element and an algebra homomorphism. Our result applies to matrix algebras, standard operator algebras, C*-algebras and W*-algebras.
Richard Aron, Pablo Galindo, Mikael Lindström (1997)
Studia Mathematica
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We prove that every weakly compact multiplicative linear continuous map from into is compact. We also give an example which shows that this is not generally true for uniform algebras. Finally, we characterize the spectra of compact composition operators acting on the uniform algebra , where is the open unit ball of an infinite-dimensional Banach space E.
H. Dales, F. Ghahramani, N. Grønbæek (1998)
Studia Mathematica
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We introduce two new notions of amenability for a Banach algebra A. The algebra A is n-weakly amenable (for n ∈ ℕ) if the first continuous cohomology group of A with coefficients in the n th dual space is zero; i.e., . Further, A is permanently weakly amenable if A is n-weakly amenable for each n ∈ ℕ. We begin by examining the relations between m-weak amenability and n-weak amenability for distinct m,n ∈ ℕ. We then examine when Banach algebras in various classes are n-weakly amenable;...
J. Bourgain (1984)
Studia Mathematica
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R. Beazer (1974)
Colloquium Mathematicae
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