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Displaying similar documents to “Solidity in sequence spaces.”

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...

The E and K functionals for the pair (X (A), l(B)).

Stefan Ericsson (1997)

Collectanea Mathematica

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We prove some exact formulas for the E and K functionals for pairs of the type (X(A),l sub ∞ (B)) where X has the lattice property. These formulas are extensions of their well-known counterparts in the scalar valued case. In particular we generalize formulas by Pisier and by the present author.

Generalized limits and a mean ergodic theorem

Yuan-Chuan Li, Sen-Yen Shaw (1996)

Studia Mathematica

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For a given linear operator L on ℓ ∞ with ∥L∥ = 1 and L(1) = 1, a notion of limit, called the L-limit, is defined for bounded sequences in a normed linear space X. In the case where L is the left shift operator on ℓ ∞ and X = ℓ ∞ , the definition of L-limit reduces to Lorentz’s definition of σ-limit, which is described by means of Banach limits on ℓ ∞ . We discuss some properties of L-limits, characterize reflexive spaces in terms of existence of L-limits of bounded sequences, and formulate a version...

Iterated series and the Hellinger-Toeplitz theorem.

Charles Swartz (1992)

Publicacions Matemàtiques

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We show that an iterated double series condition due to Antosik implies the uniform convergence of the double series. An application of Antosik's condition is given to the derivation of a vector form of the Hellinger-Toeplitz theorem.