# Journal of Operator Theory

Volume 45, Issue 1, Winter 2001 pp. 19-37.

Adapted endomorphisms which generalize Bogoljubov transformations**Authors**: Rolf Gohm

**Author institution:**Mathematisches Institut, Universitaet Tubingen, Auf der Morgenstelle 10, D-72076 Tubingen, Germany

**Summary:**We discuss a class of endomorphisms of the hyperfinite II$_1$-factor which are adapted in a certain way to a tower $\C1 \subset \C^p \subset M_p \subset M_p \otimes \C^p \subset \cdots$ so that for $p=2$ we get Bogoljubov transformations of a Clifford algebra. Results are given about surjectivity, innerness, Jones index and the shift property.

**Keywords:**Adapted, Jones tower, endomorphism, Bogoljubov transformation, inner, shift

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