Is it possible $lVert arVert =lVert 1+arVert $ in a C$^*$-algebra?
If $A$ is a unital C$^*$-algebra and $ain A$, Is it possible $
lVert a rVert =lVert 1+a rVert $ for an $ageq 0$ ?
I think it's trivial that it's not possible but I can't prove it for even $
A=Mat_{ntimes n}(mathbb{C})! $
c-star-algebras
asked Nov 20 at 12:18
Dadrahm
441112
add a comment |
If $A$ is a unital C$^*$-algebra and $ain A$, Is it possible $
lVert a rVert =lVert 1+a rVert $ for an $ageq 0$ ?
I think it's trivial that it's not possible but I can't prove it for even $
A=Mat_{ntimes n}(mathbb{C})! $
c-star-algebras
asked Nov 20 at 12:18
Dadrahm
441112
add a comment |
If $A$ is a unital C$^*$-algebra and $ain A$, Is it possible $
lVert a rVert =lVert 1+a rVert $ for an $ageq 0$ ?
I think it's trivial that it's not possible but I can't prove it for even $
A=Mat_{ntimes n}(mathbb{C})! $
c-star-algebras
asked Nov 20 at 12:18
Dadrahm
441112
If $A$ is a unital C$^*$-algebra and $ain A$, Is it possible $
lVert a rVert =lVert 1+a rVert $ for an $ageq 0$ ?
I think it's trivial that it's not possible but I can't prove it for even $
A=Mat_{ntimes n}(mathbb{C})! $
c-star-algebras
c-star-algebras
asked Nov 20 at 12:18
Dadrahm
441112
asked Nov 20 at 12:18
Dadrahm
441112
asked Nov 20 at 12:18
Dadrahm
441112
asked Nov 20 at 12:18
Dadrahm
441112
asked Nov 20 at 12:18
Dadrahm
441112
441112
add a comment |
add a comment |
1 Answer
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It is certainly not possible for $ageq 0$ since $lVert xrVert=sup sigma(x)$ for $xgeq 0$ and $sigma(1+a)=1+sigma(a)$.
answered Nov 20 at 12:21
MaoWao
2,343616
Yes. thank you. .
– Dadrahm
Nov 20 at 12:26
add a comment |
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1 Answer
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1 Answer
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oldest
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It is certainly not possible for $ageq 0$ since $lVert xrVert=sup sigma(x)$ for $xgeq 0$ and $sigma(1+a)=1+sigma(a)$.
answered Nov 20 at 12:21
MaoWao
2,343616
Yes. thank you. .
– Dadrahm
Nov 20 at 12:26
add a comment |
It is certainly not possible for $ageq 0$ since $lVert xrVert=sup sigma(x)$ for $xgeq 0$ and $sigma(1+a)=1+sigma(a)$.
answered Nov 20 at 12:21
MaoWao
2,343616
Yes. thank you. .
– Dadrahm
Nov 20 at 12:26
add a comment |
It is certainly not possible for $ageq 0$ since $lVert xrVert=sup sigma(x)$ for $xgeq 0$ and $sigma(1+a)=1+sigma(a)$.
answered Nov 20 at 12:21
MaoWao
2,343616
It is certainly not possible for $ageq 0$ since $lVert xrVert=sup sigma(x)$ for $xgeq 0$ and $sigma(1+a)=1+sigma(a)$.
answered Nov 20 at 12:21
MaoWao
2,343616
answered Nov 20 at 12:21
MaoWao
2,343616
answered Nov 20 at 12:21
MaoWao
2,343616
answered Nov 20 at 12:21
MaoWao
2,343616
2,343616
Yes. thank you. .
– Dadrahm
Nov 20 at 12:26
add a comment |
Yes. thank you. .
– Dadrahm
Nov 20 at 12:26
Yes. thank you. .
– Dadrahm
Nov 20 at 12:26
Yes. thank you. .
– Dadrahm
Nov 20 at 12:26
add a comment |
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