Vol. 44, No. 1, 1973

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Semiclosed operators

Selwyn Ross Caradus

Vol. 44 (1973), No. 1, 75–79

Elementary wellknown examples show that the sum of two closed operators need not even have a closed extension; the same is true for products, as one can see by taking the composition of maps f ffollowed by f f(0) defined on the obvious domains in C[0,1]. The natural question which then arises concerns the complexity of operators which might arise by taking repeated sums and products, starting with the closed operators. Somewhat unexpectedly, the answer is very simple: all can be reduced to products of two closed operators. Because of this, we shall distinguish this latter class by the name “semiclosed”.

Mathematical Subject Classification 2000
Primary: 47A99
Received: 8 September 1971
Published: 1 January 1973
Selwyn Ross Caradus