scholarly journals KARAKTERISTIK OPERATOR HIPONORMAL-p PADA RUANG HILBERT

2014 ◽  
Vol 6 (2) ◽  
pp. 105
Author(s):  
Gunawan Gunawan
Keyword(s):  
Hilbert Space ◽  
Partial Isometry ◽  
Positive Operators

This article discusses the definition and properties of p-hiponormal operators for p>0. To investigate the properties of p-hiponormal operators, the concept of positive operators, partial isometry operators, decomposition of operators, and existence of partial isometry operators for any operator on a Hilbert space are required.

A note on nth roots of positive operators

1969 ◽  
Vol 66 (1) ◽  
pp. 27-30
Author(s):  
John H. Jowett
Keyword(s):  
Hilbert Space ◽  
Existence And Uniqueness ◽  
Spectral Representation ◽  
Bounded Operator ◽  
Positive Operators

The existence and uniqueness of a positive self-adjoint nth. root of a positive, self-adjoint, not necessarily bounded operator on a Hilbert Space H can be readily demonstrated using the spectral representation of the transformation.

scholarly journals An operator inequality

1984 ◽  
Vol 7 (1) ◽  
pp. 205-207
Author(s):  
P. D. Siafarikas
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Positive Operators ◽  
Operator Inequality

An inequality is proved in abstract separable Hilbert spaceHwhereAandBare bounded self-adjoint positive operators defined inHsuch thatR(A)=R(B)andR(A)is closed.

scholarly journals Hilbert space structure and positive operators

2005 ◽  
Vol 305 (2) ◽  
pp. 560-565 ◽  
Author(s):  
Dimosthenis Drivaliaris ◽  
Nikos Yannakakis
Keyword(s):  
Hilbert Space ◽  
Space Structure ◽  
Positive Operators

scholarly journals Extensions of symmetric operators I: The inner characteristic function case

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
R.T.W. Martin
Keyword(s):  
Hilbert Space ◽  
Characteristic Function ◽  
Linear Transformation ◽  
Partial Isometry ◽  
Theoretic Characterization ◽  
Symmetric Operators

AbstractGiven a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic characterization of the set of all self-adjoint extensions of any symmetric linear transformation B with finite equal indices and inner Livšic characteristic function θ

Strong Extensions vs. Weak Extensions of C*-Algebras

1978 ◽  
Vol 21 (2) ◽  
pp. 143-147
Author(s):  
S. J. Cho
Keyword(s):  
Hilbert Space ◽  
Partial Isometry ◽  
Compact Operators ◽  
Bounded Operators ◽  
Infinite Dimensional ◽  
C Algebras ◽  
Infinite Dimensional Hilbert Space ◽  
Dimensional Hilbert Space ◽  
Image Position ◽  
The Ideal

Let be a separable complex infinite dimensional Hilbert space, the algebra of bounded operators in the ideal of compact operators, and the quotient map. Throughout this paper A denotes a separable nuclear C*-algebra with unit. An extension of A is a unital *-monomorphism of A into . Two extensions τ1 and τ2 are strongly (weakly) equivalent if there exists a unitary (Fredholm partial isometry) U in such thatfor all a in A.

scholarly journals The Minimum Numbers for Certain Positive Operators

2020 ◽  
Vol 12 (5) ◽  
pp. 15
Author(s):  
Ching-Yun Suen
Keyword(s):  
Hilbert Space ◽  
Lower Bounds ◽  
Positive Operators ◽  
Upper And Lower Bounds ◽  
Numerical Radius ◽  
Minimum Numbers

In this paper we give upper and lower bounds of the infimum of k  such that kI+2ReT⊗Sm  is positive, where Sm  is the m×m  matrix whose entries are all 0’s except on the superdiagonal where they are all 1’s and T∈BH  for some Hilbert space H. When T  is self-adjoint, we have the minimum of k. When m=3  and T∈B(H)  , we obtain the minimum of k  and an inequality Involving the numerical radius w(T) .

On the Mackey Borel Structure

1971 ◽  
Vol 23 (4) ◽  
pp. 674-678 ◽  
Author(s):  
L. Terrell Gardner
Keyword(s):  
Hilbert Space ◽  
Partial Isometry ◽  
Strong Topology ◽  
Partial Isometries ◽  
Infinite Dimensional ◽  
Borel Structure

Let A be a C*-algebra and a Hilbert space which is infinite dimensional and of Hilbert dimension ≧ dim π for all π ∈ Â. Suppose that the set Irr of all non-null *-representations π of A on , irreducible on the essential space , is given the relative strong topology as a subspace of Rep [2; 4; 6]. That is, the topology is that of simple convergence in with the strong topology. Finally, let ∼ denote equivalence of representations in Irr implemented by partial isometries in if and only if there exists a partial isometry with vv* ⊃ H(π1) and v*v ⊃ H(π2) satisfying π2(a) = v*π1(a)v for all a ∈ A.

The lattice structure of C*-algebras and their duals

1977 ◽  
Vol 81 (2) ◽  
pp. 245-248 ◽  
Author(s):  
Michael D. Green
Keyword(s):  
Hilbert Space ◽  
Lattice Structure ◽  
Positive Cone ◽  
Positive Operators ◽  
Partial Ordering ◽  
C Algebras ◽  
Algebra Of Operators

Let A be a *-algebra of operators on a Hilbert space H, and let Ah, A+ denote respectively the sets of self-adjoint and positive operators in A. A+ is a positive cone in Ah and it induces a partial ordering in Ah. The lattice properties of Ah were studied by R. Archbold in (1) and (2), and Chu Cho-Ho gave a different proof of some of his results in (3).

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