ar X iv : 0 70 5 . 25 76 v 2 [ m at h . O A ] 2 9 A ug 2 00 7 ADJOINTABILITY OF DENSELY DEFINED CLOSED OPERATORS AND THE MAGAJNA - SCHWEIZER THEOREM
نویسنده
چکیده
In this notes unbounded regular operators on Hilbert C∗-modules over arbitrary C∗-algebras are discussed. A densely defined operator t possesses a densely defined adjoint operator if the graph of t is an orthogonal summand. Moreover, for a densely defined operator t the graph of t is orthogonally complemented if and only if t is regular. For a given C∗-algebra A any densely defined A-linear closed operator t between Hilbert C∗modules is regular, if and only if any densely defined A-linear closed operator t between Hilbert C∗-modules admits a densely defined adjoint operator, if and only if A is a C∗algebra of compact operators. Some further characterizations of closed and regular modular operators are obtained.
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ar X iv : 0 70 5 . 25 76 v 1 [ m at h . O A ] 1 7 M ay 2 00 7 ADJOINTABILITY OF DENSELY DEFINED CLOSED OPERATORS AND THE MAGAJNA - SCHWEIZER THEOREM
In this notes unbounded regular operators on Hilbert C∗-modules over arbitrary C∗-algebras are discussed. A densely defined closed operator t possesses a densely defined adjoint operator if the graph of t is an orthogonal summand. Moreover, for a densely defined closed operator t the graph of t is orthogonally complemented if and only if t is regular. For a given C*-algebra A any densely define...
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