Abstract
AbstractWe obtain several extensions of a theorem of Shevchik which asserts that if R is a proper dense operator range in a separable Banach space E, then there exists a compact, one-to-one and dense-range operator $$T:E\rightarrow E$$
T
:
E
→
E
such that $$T(E)\cap R = \{0\}$$
T
(
E
)
∩
R
=
{
0
}
, and some results of Chalendar and Partington concerning the existence of compact, one-to-one and dense-range endomorphisms on a separable Banach space E which leave invariant a given closed subspace $$Y\subset E$$
Y
⊂
E
, or more generally, a countable increasing chain of closed subspaces of E.
Funder
Ministerio de Ciencia e Innovación
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis
Reference23 articles.
1. Abramovich, Y.A., Aliprantis, C.D.: An Invitation to Operator Theory. Graduate Studies in Mathematics, vol. 50. Amer. Math. Soc., Providence (2002)
2. Bennet, G., Kalton, N.: Inclusion theorems for $$K$$-spaces. Can. J. Math. 25, 511–524 (1973)
3. Borwein, J.M., Tingley, D.W.: On supportless convex sets. Proc. Am. Math. Soc. 94, 471–476 (1985)
4. Chalendar, I., Partington, J.: An image problem for compact operators. Proc. Am. Math. Soc. 134(5), 1391–1396 (2005)
5. Conway, J.B.: A Course in Functional Analysis. Graduate Texts in Mathematics. Springer, New York (1990)
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