Transitivity for linear operators on a Banach space

• Autorzy: Bertram Yood
• Języki publikacji: EN

Abstrakty

EN

Let G be the multiplicative group of invertible elements of E(X), the algebra of all bounded linear operators on a Banach space X. In 1945 Mackey showed that if $x_1,…,x_n$ and $y_1,…,y_n$ are any two sets of linearly independent elements of X with the same number of items, then there exists T ∈ G so that $T(x_k) = y_k$, $k = 1,…,n$. We prove that some proper multiplicative subgroups of G have this property.

Kategorie tematyczne

• 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
• 46K05: General theory of topological algebras with involution

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 132
• Numer: 3
• Strony: 239-243

Daty

wydano

1999

otrzymano

1997-04-04

Twórcy

autor

Bertram Yood

• Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802 U.S.A.

Bibliografia

• [1] S. Banach, Théorie des opérations linéaires, Warszawa, 1932.
• [2] S. R. Caradus, W. E. Pfaffenberger and B. Yood, Calkin Algebras and Algebras of Operators on Banach Spaces, Marcel Dekker, New York, 1974.
• [3] P. Civin and B. Yood, Involutions on Banach algebras, Pacific J. Math. 9 (1959), 415-436.
• [4] E. Hewitt and K. Stromberg, Real and Abstract Analysis, Springer, New York, 1965.
• [5] G. W. Mackey, On infinite-dimensional linear spaces, Trans. Amer. Math. Soc. 57 (1945), 155-207.
• [6] B. Yood, Transformations between Banach spaces in the uniform topology, Ann. of Math. 50 (1949), 486-503.