Invertible opeartors and diagonal operators
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Let $T$ be an invertible operator on an infinite dimensional Hilbert space $H$. Is there any diagonal Operator $N$ on $H$ and a unitary operator $W$ such that $WN=T$?
I know there is diagonal operator $I$ and invertible operator $T$ such that $T(I)=T$. But what about unitary equivalence?
functional-analysis operator-theory
asked Dec 2 at 5:16
saeed
17710
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up vote
0
down vote
favorite
Let $T$ be an invertible operator on an infinite dimensional Hilbert space $H$. Is there any diagonal Operator $N$ on $H$ and a unitary operator $W$ such that $WN=T$?
I know there is diagonal operator $I$ and invertible operator $T$ such that $T(I)=T$. But what about unitary equivalence?
functional-analysis operator-theory
asked Dec 2 at 5:16
saeed
17710
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $T$ be an invertible operator on an infinite dimensional Hilbert space $H$. Is there any diagonal Operator $N$ on $H$ and a unitary operator $W$ such that $WN=T$?
I know there is diagonal operator $I$ and invertible operator $T$ such that $T(I)=T$. But what about unitary equivalence?
functional-analysis operator-theory
asked Dec 2 at 5:16
saeed
17710
Let $T$ be an invertible operator on an infinite dimensional Hilbert space $H$. Is there any diagonal Operator $N$ on $H$ and a unitary operator $W$ such that $WN=T$?
I know there is diagonal operator $I$ and invertible operator $T$ such that $T(I)=T$. But what about unitary equivalence?
functional-analysis operator-theory
functional-analysis operator-theory
asked Dec 2 at 5:16
saeed
17710
asked Dec 2 at 5:16
saeed
17710
asked Dec 2 at 5:16
saeed
17710
asked Dec 2 at 5:16
saeed
17710
asked Dec 2 at 5:16
saeed
17710
17710
add a comment |
add a comment |
1 Answer
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This is not even true on finite-dimensional spaces. Then $T=WN$ implies that $T$ has orthogonal columns.
answered Dec 3 at 15:44
daw
23.9k1544
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
This is not even true on finite-dimensional spaces. Then $T=WN$ implies that $T$ has orthogonal columns.
answered Dec 3 at 15:44
daw
23.9k1544
add a comment |
up vote
0
down vote
This is not even true on finite-dimensional spaces. Then $T=WN$ implies that $T$ has orthogonal columns.
answered Dec 3 at 15:44
daw
23.9k1544
add a comment |
up vote
0
down vote
up vote
0
down vote
This is not even true on finite-dimensional spaces. Then $T=WN$ implies that $T$ has orthogonal columns.
answered Dec 3 at 15:44
daw
23.9k1544
This is not even true on finite-dimensional spaces. Then $T=WN$ implies that $T$ has orthogonal columns.
answered Dec 3 at 15:44
daw
23.9k1544
answered Dec 3 at 15:44
daw
23.9k1544
answered Dec 3 at 15:44
daw
23.9k1544
answered Dec 3 at 15:44
daw
23.9k1544
23.9k1544
add a comment |
add a comment |
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