Hostname: page-component-669899f699-tpknm Total loading time: 0 Render date: 2025-04-26T21:48:06.074Z Has data issue: false hasContentIssue false
  • English
  • Français

A spectral radius problem connected with weak compactness

Published online by Cambridge University Press:  18 May 2009

Hans-Olav Tylli
Hans-Olav Tylli
Affiliation:
Department of MathematicsUniversity of HelsinkiHallituskatu 15 SF-00100 HelsinkiFinland
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The asymptotic behaviour has been determined for several natural geometric or topological quantities related to (degrees of) compactness of bounded linear operators on Banach spaces; see for instance [24], [25] and [17]. This paper complements these results by studying the spectral properties of some quantities related to weak compactness.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 35 , Issue 1 , January 1993 , pp. 85 - 94
Copyright
Copyright © Glasgow Mathematical Journal Trust 1993

References

REFERENCES

1.Appell, J. and De Pascale, E., Su alcuni parametri connessi con la misura di non compattezza di Hausdorff in spazi di funzioni misurabili, Bollettino U.M.I. (6) 3-B (1984) 497–510.Google Scholar
2.Astala, K., On measures of noncompactness and ideal variations in Banach spaces, Ann. Acad. Sci. Fenn. Math. Diss. 29 (1980), 1–42.Google Scholar
3.Astala, K. and Tylli, H.-O., Seminorms related to weak compactness and to tauberian operators, Math. Proc. Camb. Phil. Soc. 107 (1990), 367–375.CrossRefGoogle Scholar
4.Bellenot, S., The J-sum of Banach spaces, J. Functional Analysis 48 (1982), 95–106.CrossRefGoogle Scholar
5.Buoni, J. and Klein, A., The generalized Calkin algebra, Pacific J. Math. 80 (1979), 9–12.CrossRefGoogle Scholar
6.Caradus, S. R., Pfaffenberger, W. E. and Yood, B., Calkin algebras and algebras of operators on Banach spaces, Lecture Notes Vol. 9 (Marcel Dekker, 1974).Google Scholar
7.Diestel, J., Sequences and series in Banach spaces, Graduate texts in Mathematics No. 92 (Springer-Verlag, 1984).CrossRefGoogle Scholar
8.Dowson, H. R., Spectral theory of linear operators (Academic Press, 1978).Google Scholar
9.Goldenstein, L. S., Gohberg, I. C. and Markus, A. S., Investigation of some properties of bounded linear operators in connection with their q-norm, Uch. Zap. Kishinev Gos. Univ. 29 (1957), 29–36 (Russian).Google Scholar
10.Gonzalez, M. and Onieva, V., Characterizations of tauberian operators and other semigroups of operators, Proc. Amer. Math. Soc. 108 (1990), 399–405.CrossRefGoogle Scholar
11.Gonzalez, M. and Tylli, H.-O. (in preparation).Google Scholar
12.Kalton, N. and Wilansicy, A., Tauberian operators on Banach spaces, Proc. Amer. Math. Soc. 57 (1976), 251–255.CrossRefGoogle Scholar
13.Lebow, A. and Schechter, M., Semigroups of operators and measures of noncompactness, J. Functional Analysis 7 (1971), 1–26.CrossRefGoogle Scholar
14.Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces, Lecture Notes in Mathematics No. 338 (Springer-Verlag, 1973).Google Scholar
15.Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces I, Sequence spaces (Springer-Verlag, 1977).Google Scholar
16.Makai, E. jr and Zemanek, J., The surjectivity radius, packing numbers and boundedness below of linear operators, Integral Eq. Operator Theory 6 (1983) 372–384.CrossRefGoogle Scholar
17.Rakocevic, V. and Zemanek, J., Lower s-numbers and their asymptotic behaviour, Studia Math. 91 (1988), 231–239.CrossRefGoogle Scholar
18.Tacon, D. G., Generalized semi-Fredholm transformations.J.Austral. Math. Soc. 34 (1983), 60–70.CrossRefGoogle Scholar
19.Tylli, H.-O., On the asymptotic behaviour of some quantities related to semi-Fredholm operators, J. London Math. Soc. 31 (1985), 340–348.CrossRefGoogle Scholar
20.Tylli, H.-O., Lifting non-topological divisors of zero modulo the compact operators (preprint).Google Scholar
21.Weis, L., Approximation by weakly compact operators in L 1. Math. Nachr. 119 (1984), 321–326.CrossRefGoogle Scholar
22.Weis, L. and Wolff, M., On the essential spectrum of operators on L 1, Seminarbericht Tubingen (Sommersemester 1984), 103–112.Google Scholar
23.Yang, K.-W., The generalized Fredholm operators, Trans. Amer. Math. Soc. 216 (1976), 313–326.CrossRefGoogle Scholar
24.Zemanek, J., The essential spectral radius and the Riesz part of spectrum, in Functions, Series, Operators (Proc. Intern. Conf. Budapest,1980), Colloq. Math. Soc. Janos Bolyai 35 (1983), 1275–1289.Google Scholar
25.Zemanek, J., Geometric characteristics of semi-Fredholm operators and their asymptotic behaviour, Studia Math. 80 (1984), 219–234.CrossRefGoogle Scholar