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In this work the concepts of isometries, unitaries and partial isometries operators on a Hilbert space are generalized when a semi-inner product is considered. These new concepts are described by mean of oblique projections.

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Several results on norms of projections on a Hilbert space H are extended for the operator seminorm defined by a positive semidefinite operator A ∈ L(H) + . Mathematics Subject Classification (2000). Primary 46C05; Secondary 47A05, 47A30.