scholarly journals A generalized commutativity theorem for pk-quasihyponormal operators

Filomat ◽  
2007 ◽  
Vol 21 (2) ◽  
pp. 77-83
Author(s):  
B.P. Duggal
Keyword(s):  
Hilbert Space ◽  
Generalized Derivation ◽  
Elementary Operator ◽  
Commutativity Theorem ◽  
Hilbert Space Operators

For Hilbert space operators A and B, let ?AB denote the generalized derivation ?AB(X) = AX - XB and let /\AB denote the elementary operator rAB(X) = AXB-X. If A is a pk-quasihyponormal operator, A ? pk - QH, and B*is an either p-hyponormal or injective dominant or injective pk - QH operator (resp., B*is an either p-hyponormal or dominant or pk - QH operator), then ?AB(X) = 0 =? SA*B*(X) = 0 (resp., rAB(X) = 0 =? rA*B*(X) = 0). .

scholarly journals Putnam-Fuglede theorem and the range-kernel orthogonality of derivations

2001 ◽  
Vol 27 (9) ◽  
pp. 573-582 ◽  
Author(s):  
B. P. Duggal
Keyword(s):  
Hilbert Space ◽  
Generalized Derivation ◽  
Elementary Operator ◽  
Algebra Of Operators

Letℬ(H)denote the algebra of operators on a Hilbert spaceHinto itself. Letd=δorΔ, whereδAB:ℬ(H)→ℬ(H)is the generalized derivationδAB(S)=AS−SBandΔAB:ℬ(H)→ℬ(H)is the elementary operatorΔAB(S)=ASB−S. GivenA,B,S∈ℬ(H), we say that the pair(A,B)has the propertyPF(d(S))ifdAB(S)=0impliesdA∗B∗(S)=0. This paper characterizes operatorsA,B, andSfor which the pair(A,B)has propertyPF(d(S)), and establishes a relationship between thePF(d(S))-property of the pair(A,B)and the range-kernel orthogonality of the operatordAB.

scholarly journals On an elementary operator with 2-isometric operator entries

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 5083-5088 ◽  
Author(s):  
Junli Shen ◽  
Guoxing Ji
Keyword(s):  
Hilbert Space ◽  
Generalized Derivation ◽  
Space Operator ◽  
Connected Component ◽  
Elementary Operator ◽  
Isometric Operator ◽  
Hilbert Space Operator

A Hilbert space operator T is said to be a 2-isometric operator if T*2T2- 2T*T + I = 0. Let dAB ? B(B(H)) denote either the generalized derivation ?AB = LA-RB or the elementary operator ?= LARB-I, we show that if A and B* are 2-isometric operators, then, for all complex ?, (dAB-?)-1(0)? (d*AB-?)-1(0), the ascent of (dAB-?) ? 1, and dis polaroid. Let H(?(dAB)) denote the space of functions which are analytic on ?(dAB), and let Hc(?(dAB)) denote the space of f ? H(?(dAB)) which are non-constant on every connected component of ?(dAB), it is proved that if A and B* are 2-isometric operators, then f(dAB) satisfies the generalized Weyl?s theorem and f(d*AB) satisfies the generalized a-Weyl?s theorem.

scholarly journals Bounded point evaluations for cyclic Hilbert space operators

2003 ◽  
Vol 4 (2) ◽  
pp. 301
Author(s):  
A. Bourhim
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Bounded Linear Operator ◽  
Bounded Linear ◽  
Hilbert Space Operators ◽  
Point Evaluations ◽  
Analytic Bounded Point Evaluations

<p>In this talk, to be given at a conference at Seconda Università degli Studi di Napoli in September 2001, we shall describe the set of analytic bounded point evaluations for an arbitrary cyclic bounded linear operator T on a Hilbert space H and shall answer some questions due to L. R. Williams.</p>

scholarly journals Eigenvalue inequalities for differences of means of Hilbert space operators

2012 ◽  
Vol 436 (5) ◽  
pp. 1516-1527 ◽  
Author(s):  
Omar Hirzallah ◽  
Fuad Kittaneh ◽  
Mario Krnić ◽  
Neda Lovričević ◽  
Josip Pečarić
Keyword(s):  
Hilbert Space ◽  
Hilbert Space Operators

On the p-numerical radii of Hilbert space operators

2021 ◽  
pp. 1-17
Author(s):  
Ahlem Benmakhlouf ◽  
Omar Hirzallah ◽  
Fuad Kittaneh
Keyword(s):  
Hilbert Space ◽  
Hilbert Space Operators
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