Abstract
In this book we study linear transformations (or “operators”) from a (real or com-plex) Hilbert space \(\mathfrak{H}\) into a Hilbert space\(\mathfrak{H^\prime}\); if \(\mathfrak{H}=\mathfrak{H^\prime}\) we say that the transformation (or operator) is on \(\mathfrak{H}.\) Note that if T is a bounded linear transformation from \(\mathfrak{H}\) into \(\mathfrak{H^\prime}\), then its adjoint \(\mathrm{T^*}\) is the bounded linear transformation from \(\mathfrak{H^\prime}\) into \(\mathfrak{H}\), defined by the relation
we have \(\|T\|=\|T^*\|\).
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Sz.-Nagy, B., Bercovici, H., Foias, C., Kérchy, L. (2010). Contractions and Their Dilations. In: Harmonic Analysis of Operators on Hilbert Space. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6094-8_1
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DOI: https://doi.org/10.1007/978-1-4419-6094-8_1
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