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edit approved Apr 19, 2017 at 5:58

Ali Taghavi

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Question about hereditary $C^*$-algebra.

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edited Feb 20, 2012 at 2:32

Aviv

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Can anyone give me a relatively simple proof or Some reference for the following fact.(I know that there is a proof of this theorem in Gerard J. Murphy'book: "$C^*$-Algebras and Operator Theory", but I'm sure that there should be a simple proof of this.

Every hereditary $C^*$C*-subalgebra of a simple $C^*$-algebra is also simple!

Maybe this is easy for someone, but it makes me confused for a long time. I am a novice!

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edited Feb 20, 2012 at 2:27

Aviv

147
8

Question about hereditary C$C^$-algebra.

Can anyone give me a relatively simple proof or Some reference for the following fact.(I know that there is a proof of this theorem in Gerard J. Murphy'book: "C*"$C^*$-Algebras and Operator Theory", but I'm sure that there should be a simple proof of this.

Every hereditary C-subalgebra of a simple C$C^*$-subalgebra of a simple $C^*$-algebra is also simple!

Maybe this is easy for someone, but it makes me confused for a long time. I am a novice!

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edited Feb 20, 2012 at 2:12

Aviv

147
8

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asked Feb 19, 2012 at 14:37

Aviv

147
8

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