PROPERTIES OF PURE PSEUDOREPRESENTATIONS OF COMMUTATIVE GROUPS
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We prove that a bounded pure pseudorepresentation of the group of integers Z with an arbitrarily small defect need not be an ordinary representation of the group. We also prove that a bounded pure pseudorepresentation with a sufficiently small defect of a commutative group on a dual Banach space is an ordinary representation if and only if the image of the pseudorepresentation forms a commutative family of operators.
Abstract
We prove that a bounded pure pseudorepresentation of the group of integers Z with an arbitrarily small defect need not be an ordinary representation of the group. We also prove that a bounded pure pseudorepresentation with a sufficiently small defect of a commutative group on a dual Banach space is an ordinary representation if and only if the image of the pseudorepresentation forms a commutative family of operators.
참고문헌 (4)
- A. I. Shtern, "Irreducible locally bounded finite-dimensional pseudorepresentations of connected locally compact groups", Russ. J. Math. Phys, 25(2), pp.239~240 (2018)
- A. I. Shtern, "Locally bounded finally precontinuous finite-dimensional quasirepresentations of connected locally compact groups", Mat. Sb, 208(10), pp.149~170 (2017)
- A. I. Shtern, "Continuity Conditions for Finite-Dimensional Locally Bounded Representations of Connected Locally Compact Groups", Russ. J. Math. Phys, 25(5), pp.345~382 (2018)
- A. I. Shtern, "Finite-Dimensional Quasirepresentations of Connected Lie Groups and Mishchenko’s Conjecture", Fundam. Prikl. Mat, 13(7), pp.85~225 (2007)