Hi,
This is the next problem in that theme. How can I show the following:
If we take natural embedding
then it satisfy but neither
nor
However we have .
Thanks for any help.
To me, the natural embedding of in would be the map . But in that case . Perhaps the question intends the "natural embedding" to be the map ? In that case, 0 is always in the spectrum of Tx, but it need not be in the spectrum of x.
What are and ? If they are identity elements of and , then if T is the first of the above maps, but not if T is the second map.
In that paper it is called 'natural embedding' but they didn't give any formula. When I was trying to solve this problem I took the second case witch You are mentioned.
How can I show that o need not be in the spectrum of x (in this case)?
If we take this natural embedding:
how can I show that
where and are identity elements of algebras and respectively
and that
?