Category:Positive Elements of C*-Algebras

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This category contains results about Positive Elements of C*-Algebras.
Definitions specific to this category can be found in Definitions/Positive Elements of C*-Algebras.

Let $\struct {A, \ast, \norm {\, \cdot \,} }$ be a $\text C^\ast$-algebra.

Let $x \in A$ be Hermitian.

Let $\map {\sigma_A} x$ denote the spectrum of $x$ in $A$.

We say that $x$ is positive if and only if:

$\map {\sigma_A} x \subseteq \hointr 0 \infty$

Subcategories

This category has the following 7 subcategories, out of 7 total.

C

E

Element of C*-Algebra is Positive iff Positive in Unitization‎ (2 P)

H

Hermitian Element of C*-Algebra Decomposes into Positive Elements‎ (2 P)

M

Multiple of Identity Element of Unital C*-Algebra is Positive iff Coefficient is Non-Negative Real Number‎ (2 P)

N

Non-Negative Multiple of Positive Element of C*-Algebra is Positive‎ (2 P)

S

Sum of Two Positive Elements of C*-Algebra is Positive‎ (2 P)

Pages in category "Positive Elements of C*-Algebras"

The following 24 pages are in this category, out of 24 total.

C

E

H

Hermitian Element of C*-Algebra Decomposes into Positive Elements

I

M

Multiple of Identity Element of Unital C*-Algebra is Positive iff Coefficient is Non-Negative Real Number

N

P

Q

Quotient Norm on Quotient of C*-Algebra by Closed Ideal in terms of Positive Elements of Closed Unit Ball

S

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