Browse > Article
http://dx.doi.org/10.4134/JKMS.2016.53.1.233

ANALYTIC EXTENSIONS OF M-HYPONORMAL OPERATORS  

MECHERI, SALAH (COLLEGE OF SCIENCE DEPARTMENT OF MATHEMATICS TAIBAH UNIVERSITY)
ZUO, FEI (COLLEGE OF MATHEMATICS AND INFORMATION SCIENCE HENAN NORMAL UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.53, no.1, 2016 , pp. 233-246 More about this Journal
Abstract
In this paper, we introduce the class of analytic extensions of M-hyponormal operators and we study various properties of this class. We also use a special Sobolev space to show that every analytic extension of an M-hyponormal operator T is subscalar of order 2k + 2. Finally we obtain that an analytic extension of an M-hyponormal operator satisfies Weyl's theorem.
Keywords
M-hyponormal operator; Bishop's property (${\beta}$); subscalar operator; Weyl's theorem;
Citations & Related Records
연도 인용수 순위
  • Reference
1 P. Aiena, Fredholm and Local Spectral Theory with Applications to Multipliers, Kluwer Academic Publishers, London, 2004.
2 P. Aiena, E. Aponte, and E. Balzan, Weyl type theorems for left and right polaroid operators, Integral Equations Operator Theory 66 (2010), no. 1, 1-20.   DOI
3 P. Aiena, M. Cho, and M. Gonzalez, Polaroid type operators under quasi-affinities, J. Math. Anal. Appl. 371 (2010), no. 2, 485-495.   DOI
4 S. K. Berberian, The Weyl spectrum of an operator, Indiana Univ. Math. J. 20 (1970), 529-544.   DOI
5 S. Brown, Hyponormal operators with thick spectra have invariant subspaces, Ann. of Math. 125 (1987), no. 1, 93-103.   DOI
6 X. H. Cao, Analytically class A operators and Weyl's theorem, J. Math. Anal. Appl. 320 (2006), no. 2, 795-803.   DOI
7 M. Cho and Y. M. Han, Riesz idempotent and algebraically M-hyponormal operators, Integral Equations Operator Theory 53 (2005), no. 3, 311-320.   DOI
8 H. R. Dowsow, Spectral Theory of Linear Operators, Academic Press, London, 1973.
9 N. Dunford, A survey of the theory of spectral operators, Bull. Amer. Math. Soc. 64 (1958), 217-274.   DOI
10 J. Eschmeier, Invariant subspaces for subscalar operators, Arch. Math. (Basel) 52 (1989), no. 6, 562-570.   DOI
11 J. Eschmeier, K. B. Laursen, and M. M. Neumann, Multipliers with natural local spectra on commutative Banach algebras, J. Funct. Anal. 138 (1996), no. 2, 273-294.   DOI
12 J. Eschmeier and M. Putinar, Spectral Decompositions and Analytic Sheaves, London Mathematical Society Monographs, No. 10, Clarendon Press, Oxford, 1996.
13 J. K. Han, H. Y. Lee, and W. Y. Lee, Invertible completions of $2{\times}2$ upper triangular operator matrices, Proc. Amer. Math. Soc. 128 (2000), no. 1, 119-123.   DOI
14 J. S. Han, S. H. Lee, and W. Y. Lee, On M-hyponormal weighted shifts, J. Math. Anal. Appl. 286 (2003), no. 1, 116-124.   DOI
15 R. E. Harte, Fredholm, Weyl and Browder theory, Proc. Roy. Irish Acad. 85A (1985), 151-176.
16 R. E. Harte, Invertibility and Singularity for Bounded Linear Operators, Dekker, New York, 1988.
17 J. C. Hou and X. L. Zhang, On the Weyl spectrum: Spectral mapping theorem and Weyl's theorem, J. Math. Anal. Appl. 220 (1998), no. 2, 760-768.   DOI
18 K. B. Laursen and M. M. Neumann, Automatic continuity of intertwining linear operators on Banach spaces, Rend. Circ. Mat. Palermo 40 (1991), no. 2, 325-341.   DOI
19 K. B. Laursen, An Introduction to Local Spectral Theory, London Math. Soc. Monogr. (N.S) 20, Clarendon Press, Oxford, 2000.
20 W. Y. Lee, Weyl spectra of operator matrices, Proc. Amer. Math. Soc. 129 (2001), no. 1, 131-138.   DOI
21 S. Mecheri, Bishop's property, SVEP and Dunford property (C), Electron. J. Linear Algra 23 (2012), 523-529.
22 S. Mecheri, Bishop's property and Riesz idempotent for k-quas-paranormal operators, Banach J. Math. Anal. 6 (2012), no. 1, 147-154.   DOI
23 S. Mecheri, Isolated points of spectrum of k-quasi--class A operators, Studia Math. 208 (2012), no. 1, 87-96.   DOI
24 S. Mecheri, On k-quasi-M-hyponormal operators, Math. Inequal. Appl. 16 (2013), no. 3, 895-902.
25 M. Putinar, Hyponormal operators and eigendistribution, Advances in invariant subspaces and other results of operator theory (Timioara and Herculane, 1984), 249-273, Oper. Theory Adv. Appl., 17, Birkhuser, Basel, 1986.
26 K. K. Oberai, On the Weyl spectrum, Illinois J. Math. 18 (1974), 208-212.
27 M. Oudghiri, Weyl's and Browder's theorems for operators satisfying the SVEP, Studia Math. 163 (2004), no. 1, 85-101.   DOI
28 M. Putinar, Hyponormal operators are subscalar, J. Operator Theory 12 (1984), no. 2, 385-395.
29 M. Putinar, Quasisimilarity of tuples with Bishop's property ($\beta$), Integral Equations Operator Theory 15 (1992), no. 6, 1047-1052.   DOI