PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1994 | 67 | 2 | 289-295
Tytuł artykułu

On strongly closed subalgebras of B(X)

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let X be a real or complex Banach space. The strong topology on the algebra B(X) of all bounded linear operators on X is the topology of pointwise convergence of nets of operators. It is given by a basis of neighbourhoods of the origin consisting of sets of the form (1) U(ε;x_{1},...,x_{n}) = {T ∈ B(X): ∥ Tx_{i}∥ <ε, i=1,...,n},$ where $x_{1},...,x_{n}$ are linearly independent elements of X and ε is a positive real number. Closure in the strong topology will be called strong closure for short. It is well known that the strong closure of a subalgebra of B(X) is again a subalgebra. In this paper we study strongly closed subalgebras of B(X), in particular, maximal strongly closed subalgebras. Our results are given in Section 1, while in Section 2 we give the motivation for this study and pose several open questions.
Słowa kluczowe
Rocznik
Tom
67
Numer
2
Strony
289-295
Opis fizyczny
Daty
wydano
1994
otrzymano
1994-01-21
Twórcy
autor
  • Institute of Mathematics, Polish Academy of Sciences, P.O. Box 137, 00-950 Warszawa, Poland
Bibliografia
  • [1] J. M. G. Fell and R. S. Doran, Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, Pure Appl. Math. 125 and 126, Academic Press, 1988.
  • [2] N. Jacobson, Lectures in Abstract Algebra, Vol. II, Van Nostrand, 1953.
  • [3] E. C. Nordgren, H. Radjavi and P. Rosenthal, On density of transitive algebras, Acta Sci. Math. (Szeged) 30 (1969), 175-179.
  • [4] H. Radjavi and P. Rosenthal, Invariant Subspaces, Springer, 1973.
  • [5] C. J. Read, A solution to the invariant subspace problem on the space $l_1$, Bull. London Math. Soc. 17 (1985), 305-317.
  • [6] W. Żelazko, On the problem of Fell and Doran, Colloq. Math. 62 (1991), 31-37.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv67i2p289bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.