The Cayley transform of Banach algebras.
The critical exponent of operators with constrained spectral radius
The group of commutativity preserving maps on strictly upper triangular matrices
Let be the algebra of all strictly upper triangular matrices over a unital commutative ring . A map on is called preserving commutativity in both directions if . In this paper, we prove that each invertible linear map on preserving commutativity in both directions is exactly a quasi-automorphism of , and a quasi-automorphism of can be decomposed into the product of several standard maps, which extains the main result of Y. Cao, Z. Chen and C. Huang (2002) from fields to rings.
The maximum distance between two-dimensional Banach spaces.
The structure of linear operators strongly preserving majorizations of matrices.
The structure of linear preservers of left matrix majorization on .
There is no analog of the transpose map for infinite matrices.
In this note we show that there are no ring anti-isomorphism between row finite matrix rings. As a consequence we show that row finite and column finite matrix rings cannot be either isomorphic or Morita equivalent rings. We also show that antiisomorphisms between endomorphism rings of infinitely generated projective modules may exist.