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Lipschitz-quotients and the Kunen-Martin Theorem

Yves Dutrieux (2001)

Commentationes Mathematicae Universitatis Carolinae

We show that there is a universal control on the Szlenk index of a Lipschitz-quotient of a Banach space with countable Szlenk index. It is in particular the case when two Banach spaces are Lipschitz-homeomorphic. This provides information on the Cantor index of scattered compact sets K and L such that C ( L ) is a Lipschitz-quotient of C ( K ) (that is the case in particular when these two spaces are Lipschitz-homeomorphic). The proof requires tools of descriptive set theory.

Little G. T. for lp-lattice summing operators

Mezrag, Lahcène (2006)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 46B28, 47D15.In this paper we introduce and study the lp-lattice summing operators in the category of operator spaces which are the analogous of p-lattice summing operators in the commutative case. We study some interesting characterizations of this type of operators which generalize the results of Nielsen and Szulga and we show that Λ l∞( B(H) ,OH) ≠ Λ l2( B( H) ,OH), in opposition to the commutative case.

Local algebras and the largest spectrum finite ideal.

Antonio Fernández López, Omar Jaa (1998)

Extracta Mathematicae

M. R. F. Smyth proved in [9, Theorem 3.2] that the socle of a semiprimitive Banach complex algebra coincides with the largest algebraic ideal. Later M. Benslimane, A. Kaidi and O. Jaa showed [3] the equality between the socle and the largest spectrum finite ideal in semiprimitive alternative Banach complex algebras. In fact, they showed that every spectrum finite one-sided ideal of a semiprimitive alternative Banach complex algebra is contained in the socle. In this note a new proof is given of...

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