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Rec a question

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  • Anis El Garna
    Dear Professors I d really appreciate it if you could help me with my question. Here I reformulate my question by adding some properties for the operators $A$,
    Message 1 of 2 , Feb 19, 2003
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      Dear Professors
      I'd really appreciate it if you could
      help me with my question.
      Here I reformulate my question by adding some properties for the operators
      $A$, $B$ and $V$.
      Let $E$ and $F$ be two Hilbert spaces and :
      * $A:E ---> E$, be an unbounded operator acting on $E$ with domain $D(A)$.
      * $B:F ---> F$, be an unbounded operator acting on $F$ with domain $D(B)$.
      * $V:E ---> F$, be an isometric isomorphism between $E$ and $F$ which
      verify the following properties :
      - $V(D(A))= V(D(B))$,
      - If ${x_{i}}_{i\in I}$ is a dense family in $E$ then ${V(x_{i})}_{i\in
      I}$ is a dense family in $F$,
      - $(BV)(x_{i})=(VA)(x_{i})$, forall $i\in I$ which means that $V$
      intertwines between $A$ and $B$ on a dense family of $E$, (or we say that
      $V$ transmutes $A$ into $B$ on ${x_{i}}_{i\in I}$).

      So the question is if we can get :
      $(BV)(x)=(VA)(x), \forall x\in D(A)$.

      Best regards
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