Similarity of a linear strict set-contraction and the radius of the essential spectrum

Author:
Mau-Hsiang Shih

Journal:
Proc. Amer. Math. Soc. **100** (1987), 137-139

MSC:
Primary 47A65

MathSciNet review:
883416

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Abstract | References | Similar Articles | Additional Information

Abstract: If is a bounded linear operator on a Hilbert space, define , the essential spectral radius of , by

**[1]**Felix E. Browder,*On the spectral theory of elliptic differential operators. I*, Math. Ann.**142**(1960/1961), 22–130. MR**0209909****[2]**Paul Richard Halmos,*A Hilbert space problem book*, 2nd ed., Graduate Texts in Mathematics, vol. 19, Springer-Verlag, New York-Berlin, 1982. Encyclopedia of Mathematics and its Applications, 17. MR**675952****[3]**C. Kuratowski,*Sur les espaces complets*, Fund. Math.**15**(1930), 301-309.**[4]**Richard Leggett,*Remarks on set-contractions and condensing maps*, Math. Z.**132**(1973), 361–366. MR**0346553****[5]**Roger D. Nussbaum,*The radius of the essential spectrum*, Duke Math. J.**37**(1970), 473–478. MR**0264434****[6]**Gian-Carlo Rota,*On models for linear operators*, Comm. Pure Appl. Math.**13**(1960), 469–472. MR**0112040**

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1987-0883416-2

Keywords:
Essential spectrum,
-set-contraction,
measure of noncompactness,
similarity of operators

Article copyright:
© Copyright 1987
American Mathematical Society