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Dave Benson
Dave Benson
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A possible spectral charqcterizationcharacterization of commutative $C^*$ algebras

Let $A$ be a $C^*$ algebra. Assume that the spectrum $Sp(a_1a_2\ldots a_{n-1}a_n)$ is unchanged as a set after a permutation of $a_i$'s.  (unless possible emerge or removing 0 from the spectrum) Does this imply that $A$ is a commutative algebra?What What about Banach algebra case?

A possible spectral charqcterization of commutative $C^*$ algebras

Let $A$ be a $C^*$ algebra. Assume that the spectrum $Sp(a_1a_2\ldots a_{n-1}a_n)$ is unchanged as a set after a permutation of $a_i$'s.(unless possible emerge or removing 0 from the spectrum) Does this imply that $A$ is a commutative algebra?What about Banach algebra case?

A possible spectral characterization of commutative $C^*$ algebras

Let $A$ be a $C^*$ algebra. Assume that the spectrum $Sp(a_1a_2\ldots a_{n-1}a_n)$ is unchanged as a set after a permutation of $a_i$'s.  (unless possible emerge or removing 0 from the spectrum) Does this imply that $A$ is a commutative algebra? What about Banach algebra case?

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Ali Taghavi
Ali Taghavi
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Let $A$ be a $C^*$ algebra. Assume that the spectrum $Sp(a_1a_2\ldots a_{n-1}a_n)$ is unchanged as a set after a permutation of $a_i$'s.(unless possible emerge or removing 0 from the spectrum) Does this impliesimply that $A$ is a commutative algebra?What about Banach algebra case?

Let $A$ be a $C^*$ algebra. Assume that the spectrum $Sp(a_1a_2\ldots a_{n-1}a_n)$ is unchanged as a set after a permutation of $a_i$'s.(unless possible emerge or removing 0 from the spectrum) Does this implies that $A$ is a commutative algebra?What about Banach algebra case?

Let $A$ be a $C^*$ algebra. Assume that the spectrum $Sp(a_1a_2\ldots a_{n-1}a_n)$ is unchanged as a set after a permutation of $a_i$'s.(unless possible emerge or removing 0 from the spectrum) Does this imply that $A$ is a commutative algebra?What about Banach algebra case?

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Ali Taghavi
Ali Taghavi
  • 356
  • 8
  • 31
  • 123

A possible spectral charqcterization of commutative $C^*$ algebras

Let $A$ be a $C^*$ algebra. Assume that the spectrum $Sp(a_1a_2\ldots a_{n-1}a_n)$ is unchanged as a set after a permutation of $a_i$'s.(unless possible emerge or removing 0 from the spectrum) Does this implies that $A$ is a commutative algebra?What about Banach algebra case?