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- W4302422758 abstract "We prove a general criterion for a von Neumann algebra $M$ in order to be in standard form. It is formulated in terms of an everywhere defined, invertible, antilinear, a priori not necessarily bounded operator, intertwining $M$ with its commutant $M'$ and acting as the $*$-operation on the centre. We also prove a generalized version of the BT-Theorem which enables us to see that such an intertwiner must be necessarily bounded. It is shown that this extension of the BT-Theorem leads to the automatic boundedness of quite general operators which intertwine the identity map of a von Neumann algebra with a general bounded, real linear, operator valued map. We apply the last result to the automatic boundedness of linear operators implementing algebraic morphisms of a von Neumann algebra onto some Banach algebra, and to the structure of a $W^*$-algebra $M$ endowed with a normal, semi-finite, faithful weight $varphi,$, whose left ideal $mathfrak N_{varphi}$ admits an algebraic complement in the GNS representation space $H_{varphi},$, invariant under the canonical action of $M$." @default.
- W4302422758 created "2022-10-06" @default.
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- W4302422758 date "2015-05-19" @default.
- W4302422758 modified "2023-10-17" @default.
- W4302422758 title "Quantitative BT-Theorem and automatic continuity for standard von Neumann algebras" @default.
- W4302422758 doi "https://doi.org/10.48550/arxiv.1505.04910" @default.
- W4302422758 hasPublicationYear "2015" @default.
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