Correlations of spaces of pencils

The paper introduces an axiomatic system of a conjugacy in partial linear spaces, and provides its analytical characterization in spaces of pencils. A correlation of a space of pencils is defined and it is shown to correspond to a polarity of the underlying projective space, i.e. to a reflexive sesqui-linear form, or also to an involutory collineation, i.e. to an injective semi-linear map, in the self-dual case. A geometric characterization of segment subspaces in spaces of pencils is also provided.