k -拟-*-A 类压缩算子的性质

Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (4): 823-827.

• Articles • Previous Articles Next Articles

On Properties for k-Quasi-*-class A Contractions

LI Xiao-Chun, GAO Fu-Gen

College of Mathematics and Information Science, Henan Normal University, Henan Xinxiang |453007

Received:2013-04-23 Revised:2014-03-28 Online:2014-08-25 Published:2014-08-25
Supported by:
国家自然科学基金(11301155, 11271112)、河南省教育厅科学技术研究重点项目(13B110077)、河南师范大学博士科研启动费支持课题(qd12102)和河南师范大学青年基金资助

Abstract

Abstract:

A Hilbert space operator T belongs to k-quasi-*-class A if T*^k(|T²|-|T*|²)T^k≥0. The famous Fuglede-Putnam's theorem is as follows: the operator equation AX=XB implies A*X=XB* when A and B are normal operators. In this paper, firstly we prove that if T is a contraction of k-quasi-*-class A
operators, then either T has a nontrivial invariant subspace or T is a proper contraction and the nonnegative operator D=T*^k(|T²|-|T*|²)T^kis a strongly stable contraction; secondly we prove that k-quasi-*-class A operators are not supercyclic; at last we show that if X is a Hilbert-Schmidt operator, A and (B*)^-1 are k-quasi-*-class A operators such that AX=XB, then A*X=XB*.

Key words: k-quasi-*-class A operators, Contraction operator, The Fuglede-Putnam theorem

CLC Number:

47B20 47A63

LI Xiao-Chun, GAO Fu-Gen. On Properties for k-Quasi-*-class A Contractions[J].Acta mathematica scientia,Series A, 2014, 34(4): 823-827.

Trendmd

References

[1] Aluthge A. On p-hyponormal operators for 013: 307--315

[2] Berberian S K. Note on a theorem of Fuglede and Putnam. Proc Amer Math Soc, 1959, 10: 175--182

[3] Berberian S. K. Extensions of a theorem of Fuglede-Putnam. Proc Amer Math Soc, 1978, 71: 113--114

[4] Brown A, Pearcy C. Spectra of tensor products of operators. Proc Amer Math Soc, 1966, 17: 162--166

[5] Duggal B P, Jeon I H, Kim I H. On *-paranormal contractions and properties for *-class A operators. Linear Algebra Appl, 2012, 436: 954--962

[6] Fuglede B. A commutativity theorem for normal operators. Proc Natl Acad Sci, 1950, 36: 35--40

[7] Furuta T. On the class of paranormal operators. Proc Japan Acad, 1967, 43: 594--598

[8] Furuta T. Invitation to Linear Operators. London: Taylor and Francis, 2001

[9] Furuta T, Ito M, Yamazaki T. A subclass of paranormal operators including class of log-hyponormal and several classes. Sci Math, 1998, 1(3): 389--403

[10] Furuta T. On relaxation of normality in the of Fuglede-Putnam theorem. Proc Amer Math Soc, 1979, 77: 324--328

[11] Gao F, Li X. Tensor products and the spectral continuity for k-quasi-*-class A operators. Banach J Math Anal, 2014, 8(1): 47--54

[12] Gao F, Li X. On *-class A contractions. J Inequal Appl, 2013, 243: 1--5

[13] Laursen K B, Neumann M M. Introduction to Local Spectral Theory. Oxford: Clarendon Press, 2000

[14] Mecheri S. Isolated points of spectrum of k-quasi-*-class A operators. Studia Math, 2012, 208: 87--96

[15] Mecheri S. On operators satisfying an inequality. J Inequal Appl, 2012, 244: 1--11

[16] Mecheri S, Uchiyama A. An extension of the Fuglede-Putnam's theorem to class A operators. Math Inequal Appl, 2010, 13(1): 57--61

[17] Putnam C R. On normal operators in Hilbert space. Am J Math, 1951, 73: 357--362

[18] Radjabalipour M. An extension of Fuglede-Putnam theorem for hyponormal operators. Math Zeit, 1987, 194: 117--120

[19] Rosenblum M. On a theorem of Fuglede and Putnam. J Lond Math Soc, 1958, 33: 376--377

[20] Shen J L, Zuo F, Yang C S. On operators satisfying T*|T²|T≥T*|T*|²T. Acta Math Sinica (English Ser), 2010, 26: 2109--2116

[21] Uchiyama A, Tanahashi K. Fuglede-Putnam's theorem for p-hyponormal or log-hyponormal operators. Glasgow Math J, 2002, 44: 397--410

On Properties for k-Quasi-*-class A Contractions

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 0

Metrics

Comments

Recommended 10