## Upper and lower Fredholm spectra. I

HTML articles powered by AMS MathViewer

- by John J. Buoni, Robin Harte and Tony Wickstead PDF
- Proc. Amer. Math. Soc.
**66**(1977), 309-314 Request permission

## Abstract:

Joint upper and lower Fredholm spectra are defined for*n*-tuples of bounded linear operators, and the upper Fredholm spectrum is represented both as the simultaneous eigenvalues and as the simultaneous approximate eigenvalues of an

*n*-tuple of operators obtained by a Berberian-Quigley construction.

## References

- Sterling K. Berberian,
*Approximate proper vectors*, Proc. Amer. Math. Soc.**13**(1962), 111–114. MR**133690**, DOI 10.1090/S0002-9939-1962-0133690-8 - S. R. Caradus, W. E. Pfaffenberger, and Bertram Yood,
*Calkin algebras and algebras of operators on Banach spaces*, Lecture Notes in Pure and Applied Mathematics, Vol. 9, Marcel Dekker, Inc., New York, 1974. MR**0415345** - M. D. Choi and Chandler Davis,
*The spectral mapping theorem for joint approximate point spectrum*, Bull. Amer. Math. Soc.**80**(1974), 317–321. MR**333780**, DOI 10.1090/S0002-9904-1974-13481-6 - A. T. Dash,
*Joint spectrum in the Calkin algebra*, Bull. Amer. Math. Soc.**81**(1975), no. 6, 1083–1085. MR**390800**, DOI 10.1090/S0002-9904-1975-13925-5 - Chandler Davis and Peter Rosenthal,
*Solving linear operator equations*, Canadian J. Math.**26**(1974), 1384–1389. MR**355649**, DOI 10.4153/CJM-1974-132-6 - P. A. Fillmore, J. G. Stampfli, and J. P. Williams,
*On the essential numerical range, the essential spectrum, and a problem of Halmos*, Acta Sci. Math. (Szeged)**33**(1972), 179–192. MR**322534** - Bernhard Gramsch and David Lay,
*Spectral mapping theorems for essential spectra*, Math. Ann.**192**(1971), 17–32. MR**291846**, DOI 10.1007/BF02052728 - R. E. Harte,
*Spectral mapping theorems*, Proc. Roy. Irish Acad. Sect. A**72**(1972), 89–107. MR**326394** - Arnold Lebow and Martin Schechter,
*Semigroups of operators and measures of noncompactness*, J. Functional Analysis**7**(1971), 1–26. MR**0273422**, DOI 10.1016/0022-1236(71)90041-3 - Heinrich P. Lotz,
*Über das Spektrum positiver Operatoren*, Math. Z.**108**(1968), 15–32 (German). MR**240648**, DOI 10.1007/BF01110453 - Charles E. Rickart,
*General theory of Banach algebras*, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR**0115101** - Z. Słodkowski and W. Żelazko,
*On joint spectra of commuting families of operators*, Studia Math.**50**(1974), 127–148. MR**346555**, DOI 10.4064/sm-50-2-127-148 - Vernon Williams,
*Closed Fredholm and semi-Fredholm operators, essential spectra and perturbations*, J. Functional Analysis**20**(1975), no. 1, 1–25. MR**0394276**, DOI 10.1016/0022-1236(75)90050-6

## Additional Information

- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**66**(1977), 309-314 - MSC: Primary 47A10
- DOI: https://doi.org/10.1090/S0002-9939-1977-0454676-0
- MathSciNet review: 0454676