Characterizations of generalized pencils of pairs of projections
Tóm tắt
Let T be a bounded linear operator on a complex Hilbert space
$$\mathcal {H}$$
. We present some necessary and sufficient conditions for T to be the generalized pencil
$$P + \alpha Q +\beta PQ$$
of a pair (P, Q) of projections at some point
$$(\alpha , \beta )\in \mathbb {C}^2$$
. The range and kernel relations of the generalized pencil T are studied and comments on the additional properties of some special generalized pencil are given.
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