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1998 | 68 | 1 | 27-30
Tytuł artykułu

Aspects of unconditionality of bases in spaces of compact operators

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
E. Tutaj has introduced classes of Schauder bases termed "unconditional-like" (UL) and "unconditional-like*" (UL*) whose intersection is the class of unconditional bases. In view of this association with unconditional bases, it is interesting to note that there exist Banach spaces which have no unconditional basis and yet have a basis of one of these two types (e.g., the space 𝓞[0,1]). In the same spirit, we show in this paper that the space of all compact operators on a reflexive Banach space with an unconditional basis has a basis of type UL*, even though it is well-known that this space has no unconditional basis.
Rocznik
Tom
68
Numer
1
Strony
27-30
Opis fizyczny
Daty
wydano
1998
otrzymano
1996-01-17
Twórcy
  • Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0123, U.S.A.
Bibliografia
  • [1] B. R. Gelbaum and J. Gil de Lamadrid, Bases of tensor products of Banach spaces, Pacific J. Math. 11 (1961), 1281-1286.
  • [2] S. Karlin, Bases in Banach spaces, Duke Math. J. 15 (1948), 971-985.
  • [3] J. Lindenstrauss, On a certain subspace of l¹, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 12 (1964), 539-542.
  • [4] A. Pełczyński and S. Kwapień, The main triangle projection in matrix spaces and its applications, Studia Math. 34 (1970), 43-63.
  • [5] I. Singer, Bases in Banach Spaces I, Grundlehren Math. Wiss. 154, Springer, New York, 1970.
  • [6] E. Tutaj, On Schauder bases which are unconditional-like, Bull. Polish Acad. Sci. Math. 32 (1985), 137-146.
  • [7] E. Tutaj, Some observations concerning the classes of unconditional-like basic sequences, Bull. Polish Acad. Sci. Math. 35 (1987), 35-42.
Typ dokumentu
Bibliografia
Identyfikatory
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bwmeta1.element.bwnjournal-article-apmv68z1p27bwm
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