On some properties of Banach operators. II.
Thaheem, A.B., Khan, A.R. (2004)
International Journal of Mathematics and Mathematical Sciences
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Thaheem, A.B., Khan, A.R. (2004)
International Journal of Mathematics and Mathematical Sciences
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Saccoman, John J. (2001)
International Journal of Mathematics and Mathematical Sciences
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J. Väisälä (1992)
Studia Mathematica
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We show that a normed space E is a Banach space if and only if there is no bilipschitz map of E onto E ∖ {0}.
H. G. Dales
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We modify the very well known theory of normed spaces (E,||·||) within functional analysis by considering a sequence (||·||ₙ: n ∈ ℕ) of norms, where ||·||ₙ is defined on the product space Eⁿ for each n ∈ ℕ. Our theory is analogous to, but distinct from, an existing theory of ’operator spaces’; it is designed to relate to general spaces for p ∈ [1,∞], and in particular to L¹-spaces, rather than to L²-spaces. After recalling in Chapter 1 some results in functional analysis, especially...
Nygaard, Olav (2002)
International Journal of Mathematics and Mathematical Sciences
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María D. Acosta (1995)
Extracta Mathematicae
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Cardwell, Antonia E. (2006)
International Journal of Mathematics and Mathematical Sciences
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D. Hajdukovic (1975)
Publications de l'Institut Mathématique [Elektronische Ressource]
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Antosik, Piotr, Swartz, Charles (1990)
Portugaliae mathematica
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Stanislaw Kwapien (1972)
Mémoires de la Société Mathématique de France
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Alexander Pruss (1995)
Studia Mathematica
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Let X be any topological space, and let C(X) be the algebra of all continuous complex-valued functions on X. We prove a conjecture of Yood (1994) to the effect that if there exists an unbounded element of C(X) then C(X) cannot be made into a normed algebra.
V. Rakočević (1984)
Matematički Vesnik
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Charles E. Cleaver (1972)
Colloquium Mathematicae
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Bertram Yood (2008)
Studia Mathematica
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The set of commutators in a Banach *-algebra A, with continuous involution, is examined. Applications are made to the case where A = B(ℓ₂), the algebra of all bounded linear operators on ℓ₂.