scholarly journals Some Trapezoidal Vector Inequalities for Continuous Functions of Selfadjoint Operators in Hilbert Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Dragomir
Keyword(s):  
Hilbert Spaces ◽  
Spectral Representation ◽  
Continuous Functions ◽  
Selfadjoint Operators

On utilising the spectral representation of selfadjoint operators in Hilbert spaces, some trapezoidal inequalities for various classes of continuous functions of such operators are given.

scholarly journals Parseval's equality in fuzzy normed linear spaces

Mathematica ◽  
2021 ◽  
Vol 63 (86) (1) ◽  
pp. 47-57
Author(s):  
Daraby Bayaz ◽  
Delzendeh Fataneh ◽  
Rahimi Asghar
Keyword(s):  
Hilbert Space ◽  
Vector Space ◽  
Hilbert Spaces ◽  
Continuous Functions ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Parseval’S Equality

We investigate Parseval's equality and define the fuzzy frame on Felbin fuzzy Hilbert spaces. We prove that C(Omega) (the vector space of all continuous functions on Omega) is normable in a Felbin fuzzy Hilbert space and so defining fuzzy frame on C(Omega) is possible. The consequences for the category of fuzzy frames in Felbin fuzzy Hilbert spaces are wider than for the category of the frames in the classical Hilbert spaces.

The Multidirectional Mean Value Theorem in Banach Spaces

1997 ◽  
Vol 40 (1) ◽  
pp. 88-102 ◽  
Author(s):  
M. L. Radulescu ◽  
F. H. Clarke
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Continuous Functions ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Locally Lipschitz Functions ◽  
Bump Function ◽  
Lipschitz Continuous ◽  
Lower Semi ◽  
Locally Lipschitz

AbstractRecently, F. H. Clarke and Y. Ledyaev established a multidirectional mean value theorem applicable to lower semi-continuous functions on Hilbert spaces, a result which turns out to be useful in many applications. We develop a variant of the result applicable to locally Lipschitz functions on certain Banach spaces, namely those that admit a C1-Lipschitz continuous bump function.

scholarly journals Operator Popoviciu’s inequality for superquadratic and convex functions of selfadjoint operators in Hilbert spaces

2019 ◽  
Vol 10 (4) ◽  
pp. 313-324
Author(s):  
Mohammad W. Alomari
Keyword(s):  
Hilbert Spaces ◽  
Convex Functions ◽  
Positive Operators ◽  
Selfadjoint Operators ◽  
Popoviciu’S Inequality ◽  
Linear Maps ◽  
Superquadratic Functions ◽  
Operator Version ◽  
Positive Linear Maps

AbstractIn this work, an operator version of Popoviciu’s inequality for positive operators on Hilbert spaces under positive linear maps for superquadratic functions is proved. Analogously, using the same technique, an operator version of Popoviciu’s inequality for convex functions is obtained. Some other related inequalities are also presented.

scholarly journals AN INFINITE DIMENSIONAL VERSION OF THE SCHUR CONVEXITY PROPERTY AND APPLICATIONS

2007 ◽  
Vol 05 (02) ◽  
pp. 123-136 ◽  
Author(s):  
CLAUDE VALLÉE ◽  
VICENŢIU RĂDULESCU
Keyword(s):  
Quantum Mechanics ◽  
Hilbert Spaces ◽  
Symmetric Matrix ◽  
Liouville Problem ◽  
Convexity Property ◽  
Infinite Dimensional ◽  
Selfadjoint Operators ◽  
Dimensional Version ◽  
Sturm Liouville ◽  
Schur Convexity

We extend to infinite dimensional separable Hilbert spaces the Schur convexity property of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case of linear, selfadjoint, compact operators, and that of linear selfadjoint operators that can be approximated by operators of finite rank and having a countable family of eigenvalues. The abstract results of the present paper are illustrated by several examples from mechanics or quantum mechanics, including the Sturm–Liouville problem, the Schrödinger equation, and the harmonic oscillator.

scholarly journals Fractal convolution: A new operation between functions

2019 ◽  
Vol 22 (3) ◽  
pp. 619-643
Author(s):  
María A. Navascués ◽  
Peter R. Massopust
Keyword(s):  
Hilbert Spaces ◽  
Binary Operation ◽  
Iterated Function System ◽  
Continuous Functions ◽  
Linear Operators ◽  
Function System ◽  
Fractal Function ◽  
Iterated Function

Abstract In this paper, we define an internal binary operation between functions called fractal convolution that when applied to a pair of mappings generates a fractal function. This is done by means of a suitably defined iterated function system. We study in detail this operation in 𝓛p spaces and in sets of continuous functions in a way that is different from the previous work of the authors. We develop some properties of the operation and its associated sets. The lateral convolutions with the null function provide linear operators whose characteristics are explored. The last part of the article deals with the construction of convolved fractals bases and frames in Banach and Hilbert spaces of functions.

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