Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1173.47012
Manjegani, Seyed Mahmoud
Inner spectral radius of positive operator matrices. (English)
[J] Banach J. Math. Anal. 2, No. 1, 97-104, electronic only (2008). ISSN 1735-8787/e

Let $H$ be a complex Hilbert space and $B(H)$ be the algebra of all bounded linear operators on $H$. For $a \in B(H)$, let $m(a)$, $\sigma(a)$, $W(a)$, $r(a)$, $w(a)$, $i(a)$, and $W_i(a)$ denote the minimum moduli, spectrum, numerical range, spectral radius, numerical radius, inner spectral radius and inner numerical radius of $a$, respectively. The authors give some inequalities for these. For example, if $A= (a_{ij}I)_{n\times n} \in M_n(B(H))$ and $\tilde A = (a_{ij})_{n\times n} \in M_n( \mathbb R)$ are nonnegative, then $w_i(A) \leq w_i(\tilde A)$, $m(A)\leq m(\tilde A)$ and $i(A) \leq i(\tilde A)$. Moreover, if $A= (a_{ij})_{n\times n}$ is a positive operator matrix, then $m(A) \leq \min_{1\leq i\leq n} \{m(a_{ii})\}$.
[Irfan Ul-haq (Platteville)]

MSC 2000:: *47A63 Operator inequalities, etc.
47A50 Equations and inequalities involving linear operators
47A30 Operator norms and inequalities
47A10 Spectrum and resolvent of linear operators

Keywords: minimum moduli; spectrum; numerical range; spectral radius

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]