Shape theory for C*-algebras.
Bruce Blackadar (1985)
Mathematica Scandinavica
Jaroslav Drahoš (1982)
Acta Universitatis Carolinae. Mathematica et Physica
N.Th. Varopoulos (1970)
Mathematica Scandinavica
Jesús M. F. Castillo, Yolanda Moreno (2010)
Studia Mathematica
Sobczyk's theorem asserts that every c₀-valued operator defined on a separable Banach space can be extended to every separable superspace. This paper is devoted to obtaining the most general vector valued version of the theorem, extending and completing previous results of Rosenthal, Johnson-Oikhberg and Cabello. Our approach is homological and nonlinear, transforming the problem of extension of operators into the problem of approximating z-linear maps by linear maps.
Félix Cabello Sánchez, Jesús M. Fernández Castillo, David Yost (2000)
Extracta Mathematicae
Sobczyk's theorem is usually stated as: every copy of c0 inside a separable Banach space is complemented by a projection with norm at most 2. Nevertheless, our understanding is not complete until we also recall: and c0 is not complemented in l∞. Now the limits of the phenomenon are set: although c0 is complemented in separable superspaces, it is not necessarily complemented in a non-separable superspace, such as l∞.
Michael Cwikel, Evgeniy Pustylnik (1998)
The journal of Fourier analysis and applications [[Elektronische Ressource]]
Fernando Bombal (1990)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
Manuel Valdivia, Pedro Pérez Carreras (1982)
Collectanea Mathematica
María José Rivera Ortún (1987)
Collectanea Mathematica
M. Valdivia (1979)
Journal für die reine und angewandte Mathematik
Pedro Pérez Carreras (1987)
Časopis pro pěstování matematiky
Koptev, A.V. (2004)
Sibirskij Matematicheskij Zhurnal
Manuel González, Antonio Martinón (1990)
Extracta Mathematicae
Juan A. López Molina, María José Rivera Ortún (1990)
Extracta Mathematicae
The positive and negative results related to the problem of topologies of Grothendieck [2] have given many information on the projective and injective tensor products of Fréchet and DF-spaces. The purpose of this paper is to give some results about analogous questions in αpq-Lapresté's tensor products [4, chapitre 1] and in spaces of dominated operators Pietsch [5] for a class of Fréchet spaces having a certain kind of decomposition studied dy Bonet and Díaz [1] called T-decomposition. After that...
Mehdi Nemati (2015)
Colloquium Mathematicae
We investigate some homological notions of Banach algebras. In particular, for a locally compact group G we characterize the most important properties of G in terms of some homological properties of certain Banach algebras related to this group. Finally, we use these results to study generalized biflatness and biprojectivity of certain products of Segal algebras on G.
Heikki Apiola (1976)
Studia Mathematica
A. Sersouri (1993)
Colloquium Mathematicae
For a closed subset I of the interval [0,1] we let A(I) = [v1(I),C(I)](1/2)2. We show that A(I) is isometric to a 1-complemented subspace of A(0,1), and that the Szlenk index of A(I) is larger than the Cantor index of I. We also investigate, for ordinals η < ω1, the bases structures of A(η), A*(η), and [the isometric predual of A(η)]. All the results of this paper extend, with obvious changes in the proofs, to the interpolation spaces .
Belmesnaoui Aqzzouz, M. Hassan el Alj, Redouane Nouira (2007)
RACSAM
We define the ε-product of an εb-space by quotient bornological spaces and we show that if G is a Schwartz εb-space and E|F is a quotient bornological space, then their εc-product Gεc(E|F) defined in [2] is isomorphic to the quotient bornological space (GεE)|(GεF).
D. Staszak (1992)
Collectanea Mathematica
Emmanuele, G. (1996)
Portugaliae Mathematica