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Subadditive measures on projectors of a von Neumann algebra

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Ciach L. J.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS Introduction...............................................................................................................................................5 §0. Fundamental definitions and notations...............................................................................................7 §1. Subadditive measure on projectors of a von Neumann algebra.........................................................8 §2. m-measurable operators. Convergence in measure.........................................................................10 §3. Spaces $L^a$ of m-measurable operators.......................................................................................22 §4. Some theorems on the convergence of a dominated sequence of m-measurable operators...........32 §5. Some characterizations of m-convergence.......................................................................................42 §6. Concrete examples...........................................................................................................................45 §7. Concluding remarks..........................................................................................................................60 References.............................................................................................................................................64

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1 Ciach L. J.

1 1990

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Subadditive measures on projectors of a von Neumann algebra