Banach sequence spaces

Leonard, I. E.

doi:10.1016/0022-247x(76)90248-1

Cited by 42 publications

(23 citation statements)

References 10 publications

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“…It is well known (due to Bourgain-Rosenthal in [3]) that if there is a semiembedding from a separable Banach space X to a Banach space with the Radon-Nikodym property, then X has the Radon-Nikodym property; and Leonard [16] showed that if a Banach space X has the Radon-Nikodym property, then strong p (X) also has the Radon-Nikodym property for 1 p < ∞. Note that it follows from Proposition 5 that π p (X) is separable if X is.…”

Section: So Tmentioning

confidence: 99%

The Radon–Nikodym Property for Tensor Products of Banach Lattices

Buskes

2006

Positivity

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Let 1 p < ∞. We show that p⊗F X, the Fremlin projective tensor product of p with a Banach lattice X, has the Radon-Nikodym property if and only if X has the Radon-Nikodym property; and that p⊗i X, the Wittstock injective tensor product of p with a Banach lattice X, has the Radon-Nikodym property if and only if X has the Radon-Nikodym property and each positive operator from p to X is compact, where

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Section: So Tmentioning

confidence: 99%

The Radon–Nikodym Property for Tensor Products of Banach Lattices

Buskes

2006

Positivity

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“…Note that for any sequences a, b and scalar A, we have (5) <f> n (a + b) = 4> n (a) + <t> n {b) and <j> n (\a) = \<t> n (a)-…”

Section: Notation and Definitionsmentioning

confidence: 99%

SOME SEQUENCE SPACES DEFINED BY \N,pn\ SUMMABILITY

Bhardwaj¹,

Singh²

1999

Demonstratio Mathematica

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“…We expect to have a characterization of convergent sequences in the sequence spaces of matrices in terms of some sequential convergence modes of corresponding matrix entries. In [3], I. E. Leonard gave a characterization of norm convergence of sequences in the classical Banach sequence spaces l p (X) in terms of norm convergence of sequences in the Banach space X. A similar result is also obtained in the sequence space O c .…”

Section: Sequential Convergencementioning

confidence: 77%