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 Hypo-q-Norms on a Cartesian Product of Algebras of Operators on Banach Spaces

2017 ◽  
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Banach Spaces ◽  
Cartesian Product ◽  
Schwarz Inequality ◽  
Linear Operators ◽  
Operator Norm ◽  
Numerical Radius ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Inner Products ◽  
Reverse Inequalities

In this paper we introduce the hypo-q-operator norm and hypo-q-numerical radius on a Cartesian product of algebras of bounded linear operators on Banach spaces. A representation of these norms in terms of semi-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.

scholarly journals Hypo-q-Norms on a Cartesian Product of Algebras of Operators on Banach Spaces

2020 ◽  
Vol 34 (2) ◽  
pp. 169-192
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Banach Spaces ◽  
Cartesian Product ◽  
Schwarz Inequality ◽  
Linear Operators ◽  
Operator Norm ◽  
Numerical Radius ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Inner Products ◽  
Reverse Inequalities

AbstractIn this paper we consider the hypo-q-operator norm and hypo-q-numerical radius on a Cartesian product of algebras of bounded linear operators on Banach spaces. A representation of these norms in terms of semi-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.

Three Test Problems for Quasisimilarity

1987 ◽  
Vol 39 (4) ◽  
pp. 880-892 ◽  
Author(s):  
Hari Bercovici
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Linear Operators ◽  
Structure Theory ◽  
Test Problems ◽  
Unitary Equivalence ◽  
Bounded Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Densely Defined

Kaplansky proposed in [7] three problems with which to test the adequacy of a proposed structure theory of infinite abelian groups. These problems can be rephrased as test problems for a structure theory of operators on Hilbert space. Thus, R. Kadison and I. Singer answered in [6] these test problems for the unitary equivalence of operators. We propose here a study of these problems for quasisimilarity of operators on Hilbert space. We recall first that two (bounded, linear) operators T and T′ acting on the Hilbert spaces and , are said to be quasisimilar if there exist bounded operators and with densely defined inverses, satisfying the relations T′X = XT and TY = YT′. The fact that T and T′ are quasisimilar is indicated by T ∼ T′. The problems mentioned above can now be formulated as follows.

scholarly journals WEYL TYPE THEOREMS FOR FUNCTIONS OF OPERATORS

2012 ◽  
Vol 54 (3) ◽  
pp. 493-505 ◽  
Author(s):  
SEN ZHU ◽  
CHUN GUANG LI ◽  
TING TING ZHOU
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Weyl’S Theorem ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Compact Perturbations ◽  
Weyl Type Theorems ◽  
Necessary And Sufficient

AbstractA-Weyl's theorem and property (ω), as two variations of Weyl's theorem, were introduced by Rakočević. In this paper, we study a-Weyl's theorem and property (ω) for functions of bounded linear operators. A necessary and sufficient condition is given for an operator T to satisfy that f(T) obeys a-Weyl's theorem (property (ω)) for all f ∈ Hol(σ(T)). Also we investigate the small-compact perturbations of operators satisfying a-Weyl's theorem (property (ω)) in the setting of separable Hilbert spaces.

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