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17h
comment About a property of the upper triangular projection of a matrix
In the proof, one of the parts is seeing that A does not belong to $B(\ell^2)$. In order to see this, the author states that $\infty=\lVert{I-P_T(A)}\rVert\leq \lVert{A}\rVert$. I already saw that $\infty=\lVert{I-P_T(A)}\rVert$. The inequality that remains is my doubt, I'm not sure if it is a general property or only something specific for this matrix...
17h
comment About a property of the upper triangular projection of a matrix
I edited the OP with the matrix A involved in the proof. Also, the norm I'm using is the defined as: $\lVert A\rVert_{B(\ell^2)}=\sup_{\lVert x\rVert=1}\lVert{Ax}\rVert$ ($x\in\ell^2$)
17h
revised About a property of the upper triangular projection of a matrix
added 469 characters in body
1d
comment About a property of the upper triangular projection of a matrix
Thanks for your answer Pavel. Would that mean that the property is false? I found it in a step of a proof I'm studying. I suspect maybe the author meant $(I-P_T)(B)$ instead of $I- P_T(B)$...
1d
asked About a property of the upper triangular projection of a matrix
Apr
10
asked About approximation by Haar polynomials
Mar
14
asked About Fourier multipliers
Feb
17
comment Checking if a matrix defines a bounded operator
whz, at $t=0$ we get the harmonnic series, which diverges... T.A.E., that leads us to log(1-z).
Feb
17
comment Checking if a matrix defines a bounded operator
Thanks for the answer, whz! The resulting function would be f(t)=$\displaystyle\sum_{n\in\mathbb{Z}\setminus{0}}\frac{1}{n}e^{int}$. Is it obviously bounded? I'm not sure...
Feb
17
asked Checking if a matrix defines a bounded operator
Nov
19
awarded  Yearling
Oct
29
accepted About the adjoint operator and weak operator topology.
Oct
29
comment About the adjoint operator and weak operator topology.
Thanks a lot again, Matthew. Your explanation was very clear, and I think your example works perfectly to prove the question was false.
Oct
28
comment About the adjoint operator and weak operator topology.
Thanks for your answer, Matthew! Just some doubts: why do you use double adjoints for $S_n$ and $T$, and not simple adjoints as in (2)? And where does it come the weak$^*$ to weak$^*$ continuity of $T^{**}$ (or $T^{*}$)?
Oct
28
revised About the adjoint operator and weak operator topology.
added 9 characters in body
Oct
28
comment About the adjoint operator and weak operator topology.
I just changed the notation now. Do you have in mind some example that could prove the question false?
Oct
28
revised About the adjoint operator and weak operator topology.
edited body
Oct
28
comment About the adjoint operator and weak operator topology.
Yes, you have reason, it can lead to confusion. But to avoid that here, I specificated in which spaces are the elemens in each case.
Oct
28
comment About the adjoint operator and weak operator topology.
Yes, it's the same, it's only notation, I tend to write it reverted.
Oct
28
asked About the adjoint operator and weak operator topology.