The Uniqueness of the Adjoint Operation. III

Scott H. Hochwald

The Uniqueness of the Adjoint Operation. III

Research output: Contribution to journal › Article › peer-review

Abstract

Let H be a complex, infinite-dimensional Hilbert space with inner pr (•,•)• Let B(H) denote the set of operators on H (i.e. bounded linear transformations of H into itself) and let GL(H) denote the set of invertible operators. If T e B(H) then T is positive or equivalently T > 0 means that ( Tx, x) > 0 for all x e H. The purpose of this paper is to prove the following result.

Original language	American English
Pages (from-to)	199-206
Journal	Journal of Operator Theory
Volume	20
Issue number	2
State	Published - Jan 1 1988

Keywords

Adjoints
Hilbert spaces
Mathematics
Normal operators
Real numbers
Reasoning
Semigroups
Uniqueness
complex numbers
eigenvalues

Disciplines

Applied Mathematics

Cite this

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title = "The Uniqueness of the Adjoint Operation. III",

abstract = " Let H be a complex, infinite-dimensional Hilbert space with inner pr (•,•)• Let B(H) denote the set of operators on H (i.e. bounded linear transformations of H into itself) and let GL(H) denote the set of invertible operators. If T e B(H) then T is positive or equivalently T > 0 means that ( Tx, x) > 0 for all x e H. The purpose of this paper is to prove the following result.",

keywords = "Adjoints, Hilbert spaces, Mathematics, Normal operators, Real numbers, Reasoning, Semigroups, Uniqueness, complex numbers, eigenvalues",

author = "Hochwald, {Scott H.}",

note = "HOCHWALD, S. H. (1988). THE UNIQUENESS OF THE ADJOINT OPERATION. III. Journal of Operator Theory, 20(2), 199–206.",

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language = "American English",

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AU - Hochwald, Scott H.

N1 - HOCHWALD, S. H. (1988). THE UNIQUENESS OF THE ADJOINT OPERATION. III. Journal of Operator Theory, 20(2), 199–206.

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Y1 - 1988/1/1

N2 - Let H be a complex, infinite-dimensional Hilbert space with inner pr (•,•)• Let B(H) denote the set of operators on H (i.e. bounded linear transformations of H into itself) and let GL(H) denote the set of invertible operators. If T e B(H) then T is positive or equivalently T > 0 means that ( Tx, x) > 0 for all x e H. The purpose of this paper is to prove the following result.

AB - Let H be a complex, infinite-dimensional Hilbert space with inner pr (•,•)• Let B(H) denote the set of operators on H (i.e. bounded linear transformations of H into itself) and let GL(H) denote the set of invertible operators. If T e B(H) then T is positive or equivalently T > 0 means that ( Tx, x) > 0 for all x e H. The purpose of this paper is to prove the following result.

KW - Adjoints

KW - Hilbert spaces

KW - Mathematics

KW - Normal operators

KW - Real numbers

KW - Reasoning

KW - Semigroups

KW - Uniqueness

KW - complex numbers

KW - eigenvalues

M3 - Article

SN - 0379-4024

VL - 20

SP - 199

EP - 206

JO - Journal of Operator Theory

JF - Journal of Operator Theory

IS - 2

ER -