Mixing
do we have $:leftVert Q^{n+1}xrightVert leq varepsilon leftVert Q^{n}xrightVert $ for all $xin mathcal{H}$...
$begingroup$
Let $mathcal{H}$ be a Hilbert space and let $Q$ be a bounded
quasi-nilpotent operator on $mathcal{H}$.
I'm trying to prove that for every$ varepsilon >0,$ there is some $nin
%TCIMACRO{U{2115} }%
%BeginExpansion
mathbb{N}
%EndExpansion
,$ such that $:leftVert Q^{n+1}xrightVert leq varepsilon leftVert
Q^{n}xrightVert $ for all $xin mathcal{H}$.
Thank you !
functional-analysis limits operator-theory hilbert-spaces norm
asked Feb 1 at 14:41
Djalal OunadjelaDjalal Ounadjela
29818
$endgroup$
add a comment |
$begingroup$
Let $mathcal{H}$ be a Hilbert space and let $Q$ be a bounded
quasi-nilpotent operator on $mathcal{H}$.
I'm trying to prove that for every$ varepsilon >0,$ there is some $nin
%TCIMACRO{U{2115} }%
%BeginExpansion
mathbb{N}
%EndExpansion
,$ such that $:leftVert Q^{n+1}xrightVert leq varepsilon leftVert
Q^{n}xrightVert $ for all $xin mathcal{H}$.
Thank you !
functional-analysis limits operator-theory hilbert-spaces norm
asked Feb 1 at 14:41
Djalal OunadjelaDjalal Ounadjela
29818
$endgroup$
add a comment |
$begingroup$
Let $mathcal{H}$ be a Hilbert space and let $Q$ be a bounded
quasi-nilpotent operator on $mathcal{H}$.
I'm trying to prove that for every$ varepsilon >0,$ there is some $nin
%TCIMACRO{U{2115} }%
%BeginExpansion
mathbb{N}
%EndExpansion
,$ such that $:leftVert Q^{n+1}xrightVert leq varepsilon leftVert
Q^{n}xrightVert $ for all $xin mathcal{H}$.
Thank you !
functional-analysis limits operator-theory hilbert-spaces norm
asked Feb 1 at 14:41
Djalal OunadjelaDjalal Ounadjela
29818
$endgroup$
Let $mathcal{H}$ be a Hilbert space and let $Q$ be a bounded
quasi-nilpotent operator on $mathcal{H}$.
I'm trying to prove that for every$ varepsilon >0,$ there is some $nin
%TCIMACRO{U{2115} }%
%BeginExpansion
mathbb{N}
%EndExpansion
,$ such that $:leftVert Q^{n+1}xrightVert leq varepsilon leftVert
Q^{n}xrightVert $ for all $xin mathcal{H}$.
Thank you !
functional-analysis limits operator-theory hilbert-spaces norm
functional-analysis limits operator-theory hilbert-spaces norm
asked Feb 1 at 14:41
Djalal OunadjelaDjalal Ounadjela
29818
asked Feb 1 at 14:41
Djalal OunadjelaDjalal Ounadjela
29818
asked Feb 1 at 14:41
Djalal OunadjelaDjalal Ounadjela
29818
asked Feb 1 at 14:41
Djalal OunadjelaDjalal Ounadjela
29818
asked Feb 1 at 14:41
Djalal OunadjelaDjalal Ounadjela
29818
29818
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Could this operator be a counter example? Define $T$ on $H=l^2$ as
$$
Tx =(0, frac{x_1}{2^1}, x_2, frac{x_3}{2^3}, x_4, dots ).
$$
answered Feb 3 at 12:44
dawdaw
25.1k1745
$endgroup$
$begingroup$
I will see, thank you.
$endgroup$
– Djalal Ounadjela
Feb 3 at 15:07
$begingroup$
I think it is, I will check it. Thank you
$endgroup$
– Djalal Ounadjela
Feb 3 at 15:20
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Could this operator be a counter example? Define $T$ on $H=l^2$ as
$$
Tx =(0, frac{x_1}{2^1}, x_2, frac{x_3}{2^3}, x_4, dots ).
$$
answered Feb 3 at 12:44
dawdaw
25.1k1745
$endgroup$
$begingroup$
I will see, thank you.
$endgroup$
– Djalal Ounadjela
Feb 3 at 15:07
$begingroup$
I think it is, I will check it. Thank you
$endgroup$
– Djalal Ounadjela
Feb 3 at 15:20
add a comment |
$begingroup$
Could this operator be a counter example? Define $T$ on $H=l^2$ as
$$
Tx =(0, frac{x_1}{2^1}, x_2, frac{x_3}{2^3}, x_4, dots ).
$$
answered Feb 3 at 12:44
dawdaw
25.1k1745
$endgroup$
$begingroup$
I will see, thank you.
$endgroup$
– Djalal Ounadjela
Feb 3 at 15:07
$begingroup$
I think it is, I will check it. Thank you
$endgroup$
– Djalal Ounadjela
Feb 3 at 15:20
add a comment |
$begingroup$
Could this operator be a counter example? Define $T$ on $H=l^2$ as
$$
Tx =(0, frac{x_1}{2^1}, x_2, frac{x_3}{2^3}, x_4, dots ).
$$
answered Feb 3 at 12:44
dawdaw
25.1k1745
$endgroup$
Could this operator be a counter example? Define $T$ on $H=l^2$ as
$$
Tx =(0, frac{x_1}{2^1}, x_2, frac{x_3}{2^3}, x_4, dots ).
$$
answered Feb 3 at 12:44
dawdaw
25.1k1745
answered Feb 3 at 12:44
dawdaw
25.1k1745
answered Feb 3 at 12:44
dawdaw
25.1k1745
answered Feb 3 at 12:44
dawdaw
25.1k1745
25.1k1745
$begingroup$
I will see, thank you.
$endgroup$
– Djalal Ounadjela
Feb 3 at 15:07
$begingroup$
I think it is, I will check it. Thank you
$endgroup$
– Djalal Ounadjela
Feb 3 at 15:20
add a comment |
$begingroup$
I will see, thank you.
$endgroup$
– Djalal Ounadjela
Feb 3 at 15:07
$begingroup$
I think it is, I will check it. Thank you
$endgroup$
– Djalal Ounadjela
Feb 3 at 15:20
$begingroup$
I will see, thank you.
$endgroup$
– Djalal Ounadjela
Feb 3 at 15:07
$begingroup$
I will see, thank you.
$endgroup$
– Djalal Ounadjela
Feb 3 at 15:07
$begingroup$
I think it is, I will check it. Thank you
$endgroup$
– Djalal Ounadjela
Feb 3 at 15:20
$begingroup$
I think it is, I will check it. Thank you
$endgroup$
– Djalal Ounadjela
Feb 3 at 15:20
add a comment |
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