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Math Forum » Discussions » sci.math.* » sci.math.research

Topic: Banach * Algebra
Replies: 2   Last Post: May 6, 2005 4:54 PM

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singhal.sandhya@gmail.com

Posts: 5
Registered: 3/15/05
Banach * Algebra
Posted: May 6, 2005 8:40 AM
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HI,

I am trying to solve a result, which says that
If B is a symmetric Banach * algebra and A is contained in B is also a
Banach * algebra, then for all a belongs to A,
a is invertible in B iff (aa*)/||aa*||_B and (a*a)/||a*a||_B are
invertible in B.
One way is clear but for the other part I have to show
a is invertible in B iff aa* and a*a are invertible in B.

Does anyone have any ideas for how to prove it? Any help at all would
be greatly appreciated.

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