Displaying similar documents to “On the positive absolutely summing operators on the space Lp(μ,X).”

A rigid space admitting compact operators

Paul Sisson (1995)

Studia Mathematica

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A rigid space is a topological vector space whose endomorphisms are all simply scalar multiples of the identity map. The first complete rigid space was published in 1981 in [2]. Clearly a rigid space is a trivial-dual space, and admits no compact endomorphisms. In this paper a modification of the original construction results in a rigid space which is, however, the domain space of a compact operator, answering a question that was first raised soon after the existence of complete rigid...

On invariant measures for power bounded positive operators

Ryotaro Sato (1996)

Studia Mathematica

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We give a counterexample showing that ( I - T * ) L ¯ L + = 0 does not imply the existence of a strictly positive function u in L 1 with Tu = u, where T is a power bounded positive linear operator on L 1 of a σ-finite measure space. This settles a conjecture by Brunel, Horowitz, and Lin.

Schauder decompositions and multiplier theorems

P. Clément, B. de Pagter, F. Sukochev, H. Witvliet (2000)

Studia Mathematica

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We study the interplay between unconditional decompositions and the R-boundedness of collections of operators. In particular, we get several multiplier results of Marcinkiewicz type for L p -spaces of functions with values in a Banach space X. Furthermore, we show connections between the above-mentioned properties and geometric properties of the Banach space X.