engleski

Morphisms out of a split extension of a Hilbert C*-module

Let us have a split extension W of a Hilbert C*-module V by a Hilbert C*-module Z. Like in the case of C*-algebras (well-known theorem of T. A. Loring), every morphism out of W, more precisely from W to an arbitrary Hilbert C*-module U can be described as a pair of morphisms from V and Z, respectively into U that satisfies certain conditions. It turns out that besides the generalization of the Loring's condition, an additional condition has to be posed.

HilbertC*-module; ideal submodule; (split) extension; morphism

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