scholarly journals On 2-Inner Product Spaces and Reproducing Kernel Property

2019 ◽  
Author(s):  
Saeed Hashemi Sababe
Keyword(s):  
Machine Learning ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Reproducing Kernels ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces

This paper is devoted to the study of reproducing kernels on 2-inner product Hilbert spaces. We focus on a new structure to produce reproducing kernel Hilbert and Banach spaces. According to multi-variable computing, this structures can be useful in electrocardiographs, machine learning and economy

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 REVISITING THE RECTANGULAR CONSTANT IN BANACH SPACES

2021 ◽  
pp. 1-10
Author(s):  
M. BARONTI ◽  
E. CASINI ◽  
P. L. PAPINI
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Real Banach Space ◽  
Inner Product ◽  
Two Dimensional ◽  
Product Spaces ◽  
Inner Product Spaces

Abstract Let X be a real Banach space. The rectangular constant $\mu (X)$ and some generalisations of it, $\mu _p(X)$ for $p \geq 1$ , were introduced by Gastinel and Joly around half a century ago. In this paper we make precise some characterisations of inner product spaces by using $\mu _p(X)$ , correcting some statements appearing in the literature, and extend to $\mu _p(X)$ some characterisations of uniformly nonsquare spaces, known only for $\mu (X)$ . We also give a characterisation of two-dimensional spaces with hexagonal norms. Finally, we indicate some new upper estimates concerning $\mu (l_p)$ and $\mu _p(l_p)$ .

Topologies on Generalized Inner Product Spaces

1969 ◽  
Vol 21 ◽  
pp. 158-169 ◽  
Author(s):  
Eduard Prugovečki
Keyword(s):  
Hilbert Spaces ◽  
Quantum Physics ◽  
Point Of View ◽  
Inner Product ◽  
Product Spaces ◽  
Topological Vector Spaces ◽  
Fundamental Properties ◽  
Inner Product Spaces ◽  
Algebraic Generalization ◽  
Dirac's Formalism

In the present note we introduce a straightforward algebraic generalization of inner product spaces, which we appropriately name generalized inner product (GIP) spaces. In the same fashion in which different topologies :an be introduced in inner product spaces, adequate topologies can be introduced in GIP spaces in such a manner that topological vector spaces are obtained. We enumerate and derive some fundamental properties of different topologies in GIP spaces, having primarily in mind their possible later application to quantum physics.The desirability of having in quantum physics more general structures than Hilbert spaces (in which quantum mechanics is usually formulated) is suggested by Dirac's formalism (2), which deals with “unnormalizable” vectors. Unfortunately, although this formalism is very elegant from the point of view of the facili ty of dealing with its symbolism, it completely lacks in mathematical rigour.

scholarly journals On Pompeiu Cebysev Type Inequalities for Positive Linear Maps of Selfadjoint Operators in Inner Product Spaces

2018 ◽  
Vol 15 ◽  
pp. 8081-8092
Author(s):  
Mohammad W Alomari
Keyword(s):  
Hilbert Spaces ◽  
Inner Product ◽  
Product Spaces ◽  
Selfadjoint Operators ◽  
Inner Product Spaces ◽  
Linear Maps ◽  
Positive Linear Maps

In this work, generalizations of some inequalities for continuous synchronous (h-asynchronous) functions of linear bounded selfadjoint operators under positive linear maps in Hilbert spaces are proved.

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