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On complete, precompact and compact sets.

Leonhard Frerick (1993)

Collectanea Mathematica

Completeness criterion of W. Robertson is generalized. Applications to vector valued sequences and to spaces of linear mappings are given.

On Dragilev type power Köthe spaces

P. Djakov, V. Zahariuta (1996)

Studia Mathematica

A complete isomorphic classification is obtained for Köthe spaces X = K ( e x p [ χ ( p - κ ( i ) ) - 1 / p ] a i ) such that X q d X 2 ; here χ is the characteristic function of the interval [0,∞), the function κ: ℕ → ℕ repeats its values infinitely many times, and a i . Any of these spaces has the quasi-equivalence property.

On James and Jordan-von Neumann constants and the normal structure coefficient of Banach spaces

Mikio Kato, Lech Maligranda, Yasuji Takahashi (2001)

Studia Mathematica

Some relations between the James (or non-square) constant J(X) and the Jordan-von Neumann constant C N J ( X ) , and the normal structure coefficient N(X) of Banach spaces X are investigated. Relations between J(X) and J(X*) are given as an answer to a problem of Gao and Lau [16]. Connections between C N J ( X ) and J(X) are also shown. The normal structure coefficient of a Banach space is estimated by the C N J ( X ) -constant, which implies that a Banach space with C N J ( X ) -constant less than 5/4 has the fixed point property.

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