The Parseval Theorem of the Cauchy Series and the Inner Products of Certain Hilbert Spaces

1939 ◽  
Vol 40 (1) ◽  
pp. 71
Author(s):  
Tosio Kitagawa
Keyword(s):  
Hilbert Spaces ◽  
Inner Products ◽  
Cauchy Series

scholarly journals Hypo-q-Norms on Cartesian Products of Algebras of Bounded Linear Operators on Hilbert Spaces

2017 ◽  
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Hilbert Spaces ◽  
Cartesian Product ◽  
Schwarz Inequality ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Cartesian Products ◽  
Bounded Linear ◽  
The Real ◽  
Inner Products ◽  
Reverse Inequalities

In this paper we introduce the hypo-q-norms on a Cartesian product of algebras of bounded linear operators on Hilbert spaces. A representation of these norms in terms of inner products, the equivalence with the q-norms on a Cartesian product and some reverse inequalities obtained via the scalar reverses of Cauchy-Buniakowski-Schwarz inequality are also given. Several bounds for the norms δp, ϑp and the real norms ηr,p and θr,p are provided as well.

scholarly journals Characterisation of orthogonality in certain Banach spaces

2002 ◽  
Vol 65 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Fathi B. Saidi
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Previous Article ◽  
Complex Numbers ◽  
Inner Products ◽  
Positive Integers

In this paper we adopt the notion of orthogonality introduced by the author in a previous article. We establish a characterisation for orthogonality in the spaces , where S is a set of positive integers and C is the field of complex numbers. Generalisations of the usual characterisation of orthogonality in the Hilbert spaces , via inner products, are obtained.

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

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