Numerical radius attaining operators

1985 ◽  
pp. 11-14 ◽  
Author(s):  
Carmen Silvia Cardassi
Keyword(s):  
Numerical Radius

scholarly journals THE POLYNOMIAL NUMERICAL INDEX OF A BANACH SPACE

2006 ◽  
Vol 49 (1) ◽  
pp. 39-52 ◽  
Author(s):  
Yun Sung Choi ◽  
Domingo Garcia ◽  
Sung Guen Kim ◽  
Manuel Maestre
Keyword(s):  
Banach Space ◽  
Positive Integer ◽  
Banach Spaces ◽  
Compact Space ◽  
Linear Operators ◽  
Homogeneous Polynomials ◽  
Numerical Radius ◽  
Disc Algebra ◽  
Multilinear Maps ◽  
Numerical Index

AbstractIn this paper, we introduce the polynomial numerical index of order $k$ of a Banach space, generalizing to $k$-homogeneous polynomials the ‘classical’ numerical index defined by Lumer in the 1970s for linear operators. We also prove some results. Let $k$ be a positive integer. We then have the following:(i) $n^{(k)}(C(K))=1$ for every scattered compact space $K$.(ii) The inequality $n^{(k)}(E)\geq k^{k/(1-k)}$ for every complex Banach space $E$ and the constant $k^{k/(1-k)}$ is sharp.(iii) The inequalities$$ n^{(k)}(E)\leq n^{(k-1)}(E)\leq\frac{k^{(k+(1/(k-1)))}}{(k-1)^{k-1}}n^{(k)}(E) $$for every Banach space $E$.(iv) The relation between the polynomial numerical index of $c_0$, $l_1$, $l_{\infty}$ sums of Banach spaces and the infimum of the polynomial numerical indices of them.(v) The relation between the polynomial numerical index of the space $C(K,E)$ and the polynomial numerical index of $E$.(vi) The inequality $n^{(k)}(E^{**})\leq n^{(k)}(E)$ for every Banach space $E$.Finally, some results about the numerical radius of multilinear maps and homogeneous polynomials on $C(K)$ and the disc algebra are given.

Geometric computation of the numerical radius of a matrix

2009 ◽  
Vol 52 (3) ◽  
pp. 335-353 ◽  
Author(s):  
Frank Uhlig
Keyword(s):  
Numerical Radius

scholarly journals Norm attaining and numerical radius attaining operator

1989 ◽  
Vol 2 (3) ◽  
Author(s):  
Rafael Paya ◽  
María D. Acosta
Keyword(s):  
Numerical Radius ◽  
Norm Attaining

scholarly journals Numerical Radius Inequalities in 2-Inner Product Spaces

2020 ◽  
Vol 44 (3) ◽  
pp. 415-421
Author(s):  
PANACKAL HARIKRISHNAN ◽  
◽  
HAMID REZA MORADI ◽  
MOHSEN ERFANIAN OMIDVAR ◽  
Keyword(s):  
Inner Product ◽  
Product Spaces ◽  
Numerical Radius ◽  
Inner Product Spaces

scholarly journals Matrix Young numerical radius inequalities

2013 ◽  
pp. 783-791
Author(s):  
Abbas Salemi ◽  
Alemeh Sheikhhosseini
Keyword(s):  
Numerical Radius

scholarly journals Some inequalities for the norm and the numerical radius of linear operators in Hilbert spaces

2008 ◽  
Vol 39 (1) ◽  
pp. 1-7 ◽  
Author(s):  
S. S. Dragomir
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Operator Norm ◽  
Inner Product ◽  
Product Spaces ◽  
Numerical Radius ◽  
Inner Product Spaces

In this paper various inequalities between the operator norm and its numerical radius are provided. For this purpose, we employ some classical inequalities for vectors in inner product spaces due to Buzano, Goldstein-Ryff-Clarke, Dragomir-S ´andor and the author.

scholarly journals General numerical radius inequalities for matrices of operators

2016 ◽  
Vol 14 (1) ◽  
pp. 109-117 ◽  
Author(s):  
Mohammed Al-Dolat ◽  
Khaldoun Al-Zoubi ◽  
Mohammed Ali ◽  
Feras Bani-Ahmad
Keyword(s):  
Lower Bounds ◽  
Upper Bounds ◽  
Zeros Of Polynomials ◽  
Numerical Radius

AbstractLet Ai ∈ B(H), (i = 1, 2, ..., n), and $ T = \left[ {\matrix{ 0 & \cdots & 0 & {A_1 } \cr \vdots & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {A_2 } & 0 \cr 0 & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & \vdots \cr {A_n } & 0 & \cdots & 0 \cr } } \right] $ . In this paper, we present some upper bounds and lower bounds for w(T). At the end of this paper we drive a new bound for the zeros of polynomials.

The weighted numerical radius

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Alemeh Sheikhhosseini ◽  
Maryam Khosravi ◽  
Mohammad Sababheh
Keyword(s):  
Numerical Radius
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