On inessential and improjective operators.

Pietro Aiena; Manuel González

Studia Mathematica (1998)

  • Volume: 131, Issue: 3, page 271-287
  • ISSN: 0039-3223

Abstract

top
We give several characterizations of the improjective operators, introduced by Tarafdar, and we characterize the inessential operators among the improjective operators. It is an interesting problem whether both classes of operators coincide in general. A positive answer would provide, for example, an intrinsic characterization of the inessential operators. We give several equivalent formulations of this problem and we show that the inessential operators acting between certain pairs of Banach spaces coincide with the improjective operators.

How to cite

top

Aiena, Pietro, and González, Manuel. "On inessential and improjective operators.." Studia Mathematica 131.3 (1998): 271-287. <http://eudml.org/doc/216580>.

@article{Aiena1998,
abstract = {We give several characterizations of the improjective operators, introduced by Tarafdar, and we characterize the inessential operators among the improjective operators. It is an interesting problem whether both classes of operators coincide in general. A positive answer would provide, for example, an intrinsic characterization of the inessential operators. We give several equivalent formulations of this problem and we show that the inessential operators acting between certain pairs of Banach spaces coincide with the improjective operators.},
author = {Aiena, Pietro, González, Manuel},
journal = {Studia Mathematica},
keywords = {inessential operator; improjective operator; Fredholm theory; inessential operators; improjective operators; complementability},
language = {eng},
number = {3},
pages = {271-287},
title = {On inessential and improjective operators.},
url = {http://eudml.org/doc/216580},
volume = {131},
year = {1998},
}

TY - JOUR
AU - Aiena, Pietro
AU - González, Manuel
TI - On inessential and improjective operators.
JO - Studia Mathematica
PY - 1998
VL - 131
IS - 3
SP - 271
EP - 287
AB - We give several characterizations of the improjective operators, introduced by Tarafdar, and we characterize the inessential operators among the improjective operators. It is an interesting problem whether both classes of operators coincide in general. A positive answer would provide, for example, an intrinsic characterization of the inessential operators. We give several equivalent formulations of this problem and we show that the inessential operators acting between certain pairs of Banach spaces coincide with the improjective operators.
LA - eng
KW - inessential operator; improjective operator; Fredholm theory; inessential operators; improjective operators; complementability
UR - http://eudml.org/doc/216580
ER -

References

top
  1. [1] A P. Aiena, On Riesz and inessential operators, Math. Z. 201 (1989), 521-528. Zbl0702.47008
  2. [2] P. Aiena and M. González, Essentially incomparable Banach spaces and Fredholm theory, Proc. Roy. Irish Acad. Sect. A 93 (1993), 49-59. Zbl0790.46010
  3. [3] B. Beauzamy, Introduction to Banach Spaces and Their Geometry, 2nd ed., North-Holland, Amsterdam, 1985. 
  4. [4] G M. González, On essentially incomparable Banach spaces, Math. Z. 215 (1994), 621-629. Zbl0791.46011
  5. [5] W. T. Gowers and B. Maurey, The unconditional basic sequence problem, J. Amer. Math. Soc. 6 (1993), 851-874. Zbl0827.46008
  6. [6] H. G. Heuser, Functional Analysis, Wiley, Chichester, 1982. Zbl0465.47001
  7. [7] D. Kleinecke, Almost-finite, compact, and inessential operators, Proc. Amer. Math. Soc. 14 (1963), 863-868. Zbl0117.34201
  8. [8] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I. Sequence Spaces, Springer, Berlin, 1977. Zbl0362.46013
  9. [9] A. Pietsch, Inessential operators in Banach spaces, Integral Equations Operator Theory 1 (1978), 589-591. Zbl0399.47040
  10. [10] A. Pietsch, Operator Ideals, North-Holland, Amsterdam, 1980. 
  11. [11] E. Tarafdar, Improjective operators and ideals in a category of Banach spaces, J. Austral. Math. Soc. 14 (1972), 274-292. Zbl0251.47036
  12. [12] E. Tarafdar, On further properties of improjective operators, ibid., 352-363. Zbl0251.47037
  13. [13] A. E. Taylor and D. C. Lay, Introduction to Functional Analysis, 2nd ed., Wiley, 1980. Zbl0501.46003
  14. [13] L. Weis, Perturbation classes of semi-Fredholm operators, Math. Z. 178 (1981), 429-442. Zbl0541.47010
  15. [15] R. J. Whitley, Strictly singular operators and their conjugates, Trans. Amer. Math. Soc. 113 (1964), 252-261. Zbl0124.06603

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.