scholarly journals Numerical Range of Two Operators in Semi-Inner Product Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
N. K. Sahu ◽  
C. Nahak ◽  
S. Nanda
Keyword(s):  
Point Spectrum ◽  
Numerical Range ◽  
Linear Operators ◽  
Inner Product ◽  
Product Spaces ◽  
Inclusion Relation ◽  
Nonlinear Operators ◽  
Approximate Point Spectrum ◽  
Inner Product Spaces ◽  
Inclusion Relations

In this paper, the numerical range for two operators (both linear and nonlinear) have been studied in semi-inner product spaces. The inclusion relations between numerical range, approximate point spectrum, compression spectrum, eigenspectrum, and spectrum have been established for two linear operators. We also show the inclusion relation between approximate point spectrum and closure of the numerical range for two nonlinear operators. An approximation method for solving the operator equation involving two nonlinear operators is also established.

scholarly journals Numerical Range on Weighted Hardy Spaces as Semi Inner Product Spaces

2017 ◽  
Vol 25 (1) ◽  
pp. 87-98
Author(s):  
Mohammad Taghi Heydari
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Numerical Range ◽  
Linear Operators ◽  
Inner Product ◽  
Product Spaces ◽  
Weighted Hardy Space ◽  
Weighted Hardy Spaces ◽  
Bounded Linear ◽  
Inner Product Spaces

AbstractThe semi-inner product, in the sense of Lumer, on weighted Hardy space which generate the norm is unique. Also we will discuss some properties of the numerical range of bounded linear operators on weighted Hardy spaces.

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 An algebraic characterization of complete inner product spaces

1986 ◽  
Vol 9 (1) ◽  
pp. 47-53
Author(s):  
Vasile I. Istratescu
Keyword(s):  
Banach Space ◽  
Linear Operators ◽  
Inner Product ◽  
Algebraic Characterization ◽  
Product Spaces ◽  
Bounded Linear Operators ◽  
Multiplicative Property ◽  
Bounded Linear ◽  
Inner Product Spaces

We present a characterization of complete inner product spaces using en involution on the set of all bounded linear operators on a Banach space. As a metric conditions we impose a “multiplicative” property of the norm for hermitain operators. In the second part we present a simpler proof (we believe) of the Kakutani and Mackney theorem on the characterizations of complete inner product spaces. Our proof was suggested by an ingenious proof of a similar result obtained by N. Prijatelj.

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