A NONTRIVIAL BANACH SPACE QUASIREPRESENTATION WHOSE NONZERO DEFECT OPERATORS ARE NONDEGENERATE IS BOUNDED
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We prove that every quasirepresentation T of a group G in a Banach space such that all defect operators T(g1g2) ¡ T(g1)T(g2), g1; g2 2 G, are either zero or invertible and some of them are invertible is automatically bounded. In particular, if G is amenable, then, for a sufficiently small (numerical) defect sup g1,g2∈G ||T(g1g2) - T(g1)T(g2)||, such a quasirepresentation is automatically close to an ordinary representation.
Abstract
We prove that every quasirepresentation T of a group G in a Banach space such that all defect operators T(g1g2) ¡ T(g1)T(g2), g1; g2 2 G, are either zero or invertible and some of them are invertible is automatically bounded. In particular, if G is amenable, then, for a sufficiently small (numerical) defect sup g1,g2∈G ||T(g1g2) - T(g1)T(g2)||, such a quasirepresentation is automatically close to an ordinary representation.
참고문헌 (10)
- A. I. Shtern, "Quasisymmetry. I", Russ. J. Math. Phys., 2(3), pp.353~382 (1994)
- A. I. Shtern, "Triviality and Continuity of Pseudocharacters and Pseudorepresentations", Russ. J. Math. Phys., 5(1), pp.135~138 (1998)
- A. I. Shtern, "Bounded Continuous Real 2-Cocycles on Simply Connected Simple Lie Groups and Their Applications", Russ. J. Math. Phys., 8(1), pp.122~133 (2001)
- A. I. Shtern, "Quasisymmetry. II", Russ. J. Math. Phys., 14(3), pp.332~346 (2007)
- J. A. Baker, "The stability of the equation f(x + y) =f(x)f(y)", Proc. Amer. Math. Soc., 74(2), pp.242~246 (1979)
- A. I. Shtern, "The rigidity of positive characters", Meetings of the Moscow Mathematical Society, Uspekhi Mat. Nauk, 35(5), pp.218~ (1980)
- R. Ger, "The stability of the exponential equation", Proc. Amer. Math. Soc., 124(3), pp.779~787 (1996)
- A. I. Shtern, "Exponential stability of quasihomomorphisms into Banach algebras and a Ger–Semrl theorem", Russ. J. Math. Soc., 22(1), pp.141~142 (2015)
- A. I. Shtern, "Rigidity and Approximation of Quasirepresentations of Amenable Groups", Math. Notes, 65(5–6), pp.760~769 (1999)
- H. H. Schaefer, "Topological Vector Spaces" (1999), Springer-Verlag