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A note on embedding into product spaces

M. A. Sofi (2006)

Czechoslovak Mathematical Journal

Using factorization properties of an operator ideal over a Banach space, it is shown how to embed a locally convex space from the corresponding Grothendieck space ideal into a suitable power of E , thus achieving a unified treatment of several embedding theorems involving certain classes of locally convex spaces.

Complementary triangular forms

Rob Zuidwijk (1997)

Banach Center Publications

The notion of simultaneous reduction of pairs of matrices and linear operators to triangular forms is introduced and a survey of known material on the subject is given. Further, some open problems are pointed out throughout the text. The paper is meant to be accessible to the non-specialist and does not contain any new results or proofs.

Continuity versus boundedness of the spectral factorization mapping

Holger Boche, Volker Pohl (2008)

Studia Mathematica

This paper characterizes the Banach algebras of continuous functions on which the spectral factorization mapping 𝔖 is continuous or bounded. It is shown that 𝔖 is continuous if and only if the Riesz projection is bounded on the algebra, and that 𝔖 is bounded only if the algebra is isomorphic to the algebra of continuous functions. Consequently, 𝔖 can never be both continuous and bounded, on any algebra under consideration.

Factoring Rosenthal operators.

Teresa Alvarez (1988)

Publicacions Matemàtiques

In this paper we show that a Rosenthal operator factors through a Banach space containing no isomorphs of l1.

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