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Mark Roelands
Mark Roelands
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I have a question about commutative direct summands of $C$*-algebras.

Let $A$ be a $C$*-algebra (with unit) and suppose that its bidual $A^{**}$ has a commutative direct summand, that is, $A^{**}=B\oplus C$ such that $B$ is non-trivialzero and commutative. Does this force $A$ to have a non-trivialzero commutative direct summand as well?

Thank you very much in advance for your feedback!

I have a question about commutative direct summands of $C$*-algebras.

Let $A$ be a $C$*-algebra (with unit) and suppose that its bidual $A^{**}$ has a commutative direct summand, that is, $A^{**}=B\oplus C$ such that $B$ is non-trivial and commutative. Does this force $A$ to have a non-trivial commutative direct summand as well?

Thank you very much in advance for your feedback!

I have a question about commutative direct summands of $C$*-algebras.

Let $A$ be a $C$*-algebra (with unit) and suppose that its bidual $A^{**}$ has a commutative direct summand, that is, $A^{**}=B\oplus C$ such that $B$ is non-zero and commutative. Does this force $A$ to have a non-zero commutative direct summand as well?

Thank you very much in advance for your feedback!

Source Link
Mark Roelands
Mark Roelands
  • 633
  • 3
  • 10

Commutative direct summands of C*-algebras

I have a question about commutative direct summands of $C$*-algebras.

Let $A$ be a $C$*-algebra (with unit) and suppose that its bidual $A^{**}$ has a commutative direct summand, that is, $A^{**}=B\oplus C$ such that $B$ is non-trivial and commutative. Does this force $A$ to have a non-trivial commutative direct summand as well?

Thank you very much in advance for your feedback!