| Title:
|
Linear inessential operators and generalized inverses (English) |
| Author:
|
Barnes, Bruce A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
75-82 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The space of inessential bounded linear operators from one Banach space $X$ into another $Y$ is introduced. This space, $I(X,Y)$, is a subspace of $B(X,Y)$ which generalizes Kleinecke's ideal of inessential operators. For certain subspaces $W$ of $\,I(X,Y)$, it is shown that when $T\in B(X,Y)$ has a generalized inverse modulo $W$, then there exists a projection $P\in B(X)$ such that $T(I-P)$ has a generalized inverse and $TP\in W$. (English) |
| Keyword:
|
inessential operator |
| Keyword:
|
Fredholm operator |
| Keyword:
|
generalized inverse |
| MSC:
|
47A05 |
| MSC:
|
47A55 |
| idZBL:
|
Zbl 1212.47001 |
| idMR:
|
MR2562804 |
| . |
| Date available:
|
2009-08-18T12:23:05Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133415 |
| . |
| Reference:
|
[AA] Abramovich Y., Aliprantis C.: An Invitation to Operator Theory.Graduate Studies in Math. 50, American Mathematical Society, Providence, 2002. Zbl 1022.47001, MR 1921782 |
| Reference:
|
[B] Barnes B.: Generalized inverses of operators in some subalgebras of $B(X)$.Acta Sci. Math. (Szeged) 69 (2003), 349--357. Zbl 1063.47029, MR 1991672 |
| Reference:
|
[BMSW] Barnes B., Murphy G., Smyth R., and West T.T.: Riesz and Fredholm Theory in Banach Algebras.Research Notes in Mathematics 67, Pitman, Boston, 1982. MR 0668516 |
| Reference:
|
[C] Caradus S.: Generalized Inverses and Operator Theory.Queen's Papers in Pure and Applied Math. 50, Queen's University, Kingston, Ont., 1978. Zbl 0434.47003, MR 0523736 |
| Reference:
|
[CPY] Caradus S., Pfaffenberger W., Yood B.: Calkin Algebras and Algebras of Operators on Banach Spaces.Lecture Notes in Pure and Applied Math., Vol. 9, Marcel Dekker, New York, 1974. Zbl 0299.46062, MR 0415345 |
| Reference:
|
[J] Jörgens K.: Linear Integral Operators.Pitman, Boston, 1982. MR 0647629 |
| Reference:
|
[K] Kleinecke D.: Almost finite, compact, and inessential operators.Proc. Amer. Math. Soc. 14 (1963), 863--868. Zbl 0117.34201, MR 0155197, 10.1090/S0002-9939-1963-0155197-5 |
| Reference:
|
[LT] Lay D., Taylor A.: Introduction to Functional Analysis.John Wiley and Sons, New York, 1980. Zbl 0654.46002, MR 0564653 |
| Reference:
|
[P] Palmer T.: Banach Algebras and the General Theory of *-Algebras, Vol. 1.Encyclopedia of Mathematics and its Applications 49, Cambridge University Press, Cambridge, 1994. MR 1270014 |
| Reference:
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[R] Rakočević V.: A note on regular elements in Calkin algebras.Collect. Math. 43 (1992), 37--42. MR 1214221 |
| . |
