# On inessential and improjective operators.

Studia Mathematica (1998)

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

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

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