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Dilations of Hilbert space operators (General theory)

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Mlak W.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS Introduction ........................................................................................................... 5 1. Notation and definitions.......................................................................................... 7 2. Elementary properties of dilations........................................................................ 8 3. Semi-groups and their representations ............................................................. 9 4. Minimality and uniqueness of dilations............................................................... 13 5. Positive definite operator valued functions ........................................................ 17 6. General existence theorems................................................................................. 23 7. Positive definite functions on groups................................................................... 32 8. Intertwining operators for dilatable operator functions..................................... 37 9. Dilations of operator functions on star algebras................................................ 44 References.................................................................................................................... 60

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1 Mlak W.

1 1978

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Dilations of Hilbert space operators (General theory)