Aspects of unconditionality of bases in spaces of compact operators

• Autorzy: James R. Holub
• 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.

Słowa kluczowe

EN

unconditional basis; unconditional-like basis; tensor product basis; compact operator space

Kategorie tematyczne

• 46E40: Spaces of vector- and operator-valued functions
• 46B15: Summability and bases

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1998
• Tom: 68
• Numer: 1
• Strony: 27-30

Daty

wydano

1998

otrzymano

1996-01-17

Twórcy

autor

James R. Holub

• 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.