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On different products of closed operators. (English) Zbl 1151.47004
Advantages and disadvantages of the usual product of two closed operators in a complex Hilbert space and of the product in the Dixmier sense are considered. In order to overcome these disadvantages, the authors introduce a new product by means of some Labrousse–Mercier results. This product is associative, but non-commutative and it does not have the identity. However, an adjoint of that product is a product of adjoints. Also, that product is bounded whenever at least one of its components is bounded.
MSC:
47A05General theory of linear operators