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Closed linear operators with domain containing their range

Published online by Cambridge University Press:  20 January 2009

Schôichi Ôta
Schôichi Ôta
Affiliation:
Department of Mathematics, Kyushu University 33, Fukuoka 812, Japan
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In connection with algebras of unbounded operators, Lassner showed in [4] that, if T is a densely defined, closed linear operator in a Hilbert space such that its domain is contained in the domain of its adjoint T* and is globally invariant under T and T*,then T is bounded. In the case of a Banach space (in particular, a C*-algebra) weshowed in [6] that a densely defined closed derivation in a C*-algebra with domaincontaining its range is automatically bounded (see the references in [6] and [7] for thetheory of derivations in C*-algebras).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 27 , Issue 2 , June 1984 , pp. 229 - 233
Copyright
Copyright © Edinburgh Mathematical Society 1984

References

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