A Note On The Maximal Numerical Range Of The Bimultiplication M2,A,B

被引：0

作者：

Baghdad, A. ^{[1
]}

Kaadoud, M. C. ^{[1
]}

机构：

[1] Cadi Ayyad Univ, FFSM, Dept Math, Marrakech, Morocco

来源：

JOURNAL OF MATHEMATICAL EXTENSION | 2022年 / 16卷 / 04期

关键词：

Numerical range; maximal numerical range; normal operator; hyponormal operator; elementary operators; NORM;

D O I：

10.30495/JME.2022.1884

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let B(H) denote the algebra of all bounded linear operators acting on a complex Hilbert space H. For A, B is an element of B(H), define the bimultiplication operator M-2,M-A,M-B on the class of Hilbert-Schmidt operators by M-2,M-A,M-B (X) = AXB. In this paper, we show that if B*, the adjoint operator of B, is hyponormal, then co(W-0(A)W-0(B)) subset of W-0(M-2,M-A,M-B), where co stands for the convex hull and W-0(.) denotes the maximal numerical range. If in addition, A is hyponormal, we show that co(W-0(A)W-0(B)) = W-0(M-2,M-A,M-B).

引用

页数：12

共 18 条

[1] Aupetit B., 1991, A Primer on Spectral Theory
[2] ON THE MAXIMAL NUMERICAL RANGE OF A HYPONORMAL OPERATOR
Baghdad, Abderrahim
Kaadoud, Mohamed Chraibi
[J]. OPERATORS AND MATRICES, 2019, 13 (04): : 1163 - 1171
[3] BONSALL F., 1973, London Math. Soc. Lecture Note Series, V10
[4] Bonsall F. F., 1971, London Math. Soc. Lecture Notes Series, V2
[5] A NOTE CONCERNING THE NUMERICAL RANGE OF A BASIC ELEMENTARY OPERATOR
Boumazgour, Mohamed
Nabwey, Hossam A.
[J]. ANNALS OF FUNCTIONAL ANALYSIS, 2016, 7 (03): : 434 - 441
[6] Conway JB., 2000, COURSE OPERATOR THEO
[7] FIALKOW LA, 1992, ELEMENTARY OPERATORS & APPLICATIONS, IN MEMORY OF DOMINGO A HERRERO, P55
[8] FONG CK, 1979, ACTA SCI MATH, V41, P307
[9] Numerical Radii for Tensor Products of Operators
Gau, Hwa-Long
Wang, Kuo-Zhong
Wu, Pei Yuan
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 2014, 78 (03) : 375 - 382
[10] Gustafson K. E., 1997, Numerical range.

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