Numerical Range in C-Algebras
Let A be a C*-algebra with unit 1 and let S be the state space of A, i.e., S = {ϕ ∈ A∗ : ϕ > 0, ϕ(1) = 1}. For each a ∈ A, the C*-algebra numerical range is defined by V (a) := {ϕ(a) : ϕ ∈ S}. We prove that if V (a) is a disc with center at the origin, then ka+a ∗ k = ka − a ∗ k...
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| Published in | Journal of Mathematical Extension Vol. 6; no. 2; pp. 91 - 98 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Islamic Azad University
01.06.2012
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| Online Access | Get full text |
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| Summary: | Let A be a C*-algebra with unit 1 and let S be the state space of A, i.e., S = {ϕ ∈ A∗ : ϕ > 0, ϕ(1) = 1}. For each a ∈ A, the C*-algebra numerical range is defined by V (a) := {ϕ(a) : ϕ ∈ S}. We prove that if V (a) is a disc with center at the origin, then ka+a ∗ k = ka − a ∗ k |
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| ISSN: | 1735-8299 1735-8299 |