Browse > Article
http://dx.doi.org/10.4134/JKMS.2006.43.4.899

ON WEYL'S THEOREM FOR QUASI-CLASS A OPERATORS  

Duggal Bhagwati P. (8 Redwood Grove Northfields Avenue)
Jeon, In-Ho (Department of Mathematics Education Seoul National University of Education)
Kim, In-Hyoun (Department of Mathematics Seoul National University)
Publication Information
Journal of the Korean Mathematical Society / v.43, no.4, 2006 , pp. 899-909 More about this Journal
Abstract
Let T be a bounded linear operator on a complex infinite dimensional Hilbert space $\scr{H}$. We say that T is a quasi-class A operator if $T^*\|T^2\|T{\geq}T^*\|T\|^2T$. In this paper we prove that if T is a quasi-class A operator and f is a function analytic on a neigh-borhood or the spectrum or T, then f(T) satisfies Weyl's theorem and f($T^*$) satisfies a-Weyl's theorem.
Keywords
quasi-class A operators; Weyl's theorem; a-Weyl's theorem; a-Browder theorem;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 10  (Related Records In Web of Science)
Times Cited By SCOPUS : 11
연도 인용수 순위
1 L. A. Coburn, Weyl's theorem for nonnormal operators, Michigan Math. J. 13 (1966), 285-288   DOI
2 S. V. Djordjevic and Y. M. Han, Browder's theorem and spectral continuity, Glasgow Math. J. 42 (2000), no. 3, 479-486   DOI
3 R. E. Harte and W. Y. Lee, Another note on Weyl's theorem, Trans. Amer. Math. Soc. 349 (1997), no. 5, 2115-2124   DOI   ScienceOn
4 H. Heuser, Functional Analysis, Marcel Dekker, New York, 1982
5 I. H. Jeon, Weyl's theorem and quasi-similarity, Integral Equations Operator Theory 39 (2001), no. 2, 214-221   DOI
6 I. H. Jeon, J. I. Lee and A. Uchiyama, On p-quasihyponormal operators and quasisimilarity, Math. Ineq. Appl. 6 (2003), no. 2, 309-315
7 K. B. Laursen and M. N. Neumann, Introduction to local spectral theory, Claren- don Press, Oxford, 2000
8 W. Y. Lee, Weyl spectra of operator matrices, Proc. Amer. Math. Soc. 129 (2001), no. 1, 131-138
9 C. A. McCarthy, $c_\rho$, Israel J. Math. 5 (1967), 249-271   DOI
10 C. Schmoeger, The spectral mapping theorem for the essentail approximate point spectrum, Collquium Math. 74 (1997), 167-176
11 A. Uchiyama, Inequalities of Putnam and Berger-Shaw for p-quasihyponormal operators, Integral Equations Operator Theory 34 (1999), no. 1, 91-106   DOI
12 T. Furuta, M. Ito and T. Yamazaki, A subclass of paranormal operators including class of log-hyponormal and several related classes, Scientiae Mathematicae 1 (1998), 389-403
13 R. E. Harte, Invertibility and Singularity for Bounded Linear Operators, Marcel Dekker, New York, 1988
14 A. Uchiyama, Weyl's theorem for class A operators, Math. Inequal. Appl. 4 (2001), no. 1, 143-150
15 A. Uchiyama and S. V. Djordjevic, Weyl's theorem for p-quasihyponormal operators (preprint)
16 W. Y. Lee and S. H. Lee, A spectral mapping theorem for the Weyl spectrum, Glasgow Math. J. 38 (1996), no. 1, 61-64   DOI
17 P. Aiena, C. Carpintero and E. Rosas, Some characterizations of operators sat- isfying a-Browder's theorem, J. Math. Anal. Appl. 311 (2005), no. 2, 530-544   DOI   ScienceOn
18 B. P. Duggal, Hereditarily normaloid operators, Extracta Math. 20 (2005), 203- 217
19 V. Rakocevic, On one subset of M. Scechter's essential spectrum, Mat. Vesnik 5 (1981), no. 4, 389-391
20 A. Aluthge, On p-hyponormal operators for 0 < p < 1, Integral Equations Oper- ator Theory 13 (1990), no. 3, 307-315   DOI
21 V. Rakocevic, Operators obeying a-Weyl's theorem, Rev. Roumaine Math. Pures Appl. 34 (1989), no. 10, 915-919
22 I. H. Jeon and B. P. Duggal, On operators with an absolute value condition, J. Korean Math. Soc. 41 (2004), no. 4, 617-627   과학기술학회마을   DOI   ScienceOn
23 I. H. Jeon and I. H. Kim, On operators satisfying $T*\midT^2\midT\geqT*\midT^2\midT$, Lin. Alg. Appl. (to appear)
24 W. Y. Lee, Weyl's theorem for operator matrices, Integral Equations Operator Theory 32 (1998), 319-331   DOI
25 M. Cho and T. Yamazaki, An operator transform from class A to the class of hyponormal operators and its application, Integral Equations Operator Theory 53 (2005), 497-508   DOI
26 B. P. Duggal, Weyl's theorem for totally hereditarily normaloid operators, Rend. Circ. Mat. Palermo (2) 53 (2004), no. 3, 417-428   DOI
27 T. Furuta, Invitation to Linear Operators, Taylor and Francis, London, 2001
28 P. Aiena, Classes of operators satisfying a-Weyl's theorem, Studia Math. 169 (2005), no. 2, 105-122   DOI