Browse > Article
http://dx.doi.org/10.4134/JKMS.2010.47.2.351

WEYL'S THEOREM AND TENSOR PRODUCT FOR OPERATORS SATISFYING T*k|T2|Tk≥T*k|T|2Tk  

Kim, In-Hyoun (Department of Mathematics, University of Incheon)
Publication Information
Journal of the Korean Mathematical Society / v.47, no.2, 2010 , pp. 351-361 More about this Journal
Abstract
For a bounded linear operator T on a separable complex infinite dimensional Hilbert space $\mathcal{H}$, we say that T is a quasi-class (A, k) operator if $T^{*k}|T^2|T^k\;{\geq}\;T^{*k}|T|^2T^k$. In this paper we prove that if T is a quasi-class (A, k) operator and f is an analytic function on an open neighborhood of the spectrum of T, then f(T) satisfies Weyl's theorem. Also, we consider the tensor product for quasi-class (A, k) operators.
Keywords
quasi-class (A, k) operator; Weyl's theorem; tensor product;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
연도 인용수 순위
1 I. H. Kim, Tensor products of log-hyponormal operators, Bull. Korean Math. Soc. 42 (2005), no. 2, 269–277.
2 T. Ando, Operators with a norm condition, Acta Sci. Math. (Szeged) 33 (1972), 169–178.
3 S. K. Berberian, An extension of Weyl's theorem to a class of not necessarily normal operators, Michigan Math. J. 16 (1969), 273–279.   DOI
4 L. A. Coburn, Weyl's theorem for nonnormal operators, Michigan Math. J. 13 (1966), 285–288.   DOI
5 B. P. Duggal, Weyl's theorem for totally hereditarily normaloid operators, Rend. Circ. Mat. Palermo (2) 53 (2004), no. 3, 417–428.   DOI
6 B. P. Duggal, I. H. Jeon, and I. H. Kim, On Weyl's theorem for quasi-class A operators, J. Korean Math. Soc. 43 (2006), no. 4, 899–909.   DOI   ScienceOn
7 T. Furuta, M. Ito, and T. Yamazaki, A subclass of paranormal operators including class of log-hyponormal and several related classes, Sci. Math. 1 (1998), no. 3, 389–403
8 R. E. Harte, Invertibility and Singularity for Bounded Linear Operators, Monographs and Textbooks in Pure and Applied Mathematics, 109. Marcel Dekker, Inc., New York, 1988.
9 J.-C. Hou, On the tensor products of operators, Acta Math. Sinica (N.S.) 9 (1993), no. 2, 195–202.   DOI   ScienceOn
10 I. H. Jeon and B. P. Duggal, On operators with an absolute value condition, J. Korean Math. Soc. 41 (2004), no. 4, 617–627.   DOI   ScienceOn
11 I. H. Jeon and I. H. Kim, On operators satisfying $T^{\ast}|T^2|T{\geq}T^{\ast}|T|^2T$, Linear Algebra Appl. 418 (2006), no. 2-3, 854–862.   DOI   ScienceOn
12 W. Y. Lee, Weyl's theorem for operator matrices, Integral Equations Operator Theory 32 (1998), no. 3, 319–331.   DOI
13 W. Y. Lee, Weyl spectra of operator matrices, Proc. Amer. Math. Soc. 129 (2001), no. 1, 131–138   DOI   ScienceOn
14 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
15 A. Uchiyama, Weyl's theorem for class A operators, Math. Inequal. Appl. 4 (2001), no. 1, 143–150.
16 T. Saito, Hyponormal operators and related topics, Lectures on operator algebras (dedicated to the memory of David M. Topping; Tulane Univ. Ring and Operator Theory Year, 1970–1971, Vol. II), pp. 533–664. Lecture Notes in Math., Vol. 247, Springer, Berlin, 1972.
17 J. Stochel, Seminormality of operators from their tensor product, Proc. Amer. Math. Soc. 124 (1996), no. 1, 135–140.   DOI   ScienceOn
18 K. Tanahashi, I. H. Jeon, I. H. Kim, and A. Uchiyama, Quasinilpotent part of class A or (p, k)-quasihyponormal operators (preprint).
19 A. Uchiyama and S. V. Djordjevic, Weyls theorem for p-quasihyponormal operators (preprint).
20 H. Weyl, Uber beschrankte quadratische Formen, deren Differenz vollsteig ist, Rend. Circ. Mat. Palermo 27 (1909), 373–392.   DOI