Algebraic spectral subspaces and automatic continuity

Spectral measures and automatic continuity

Let X be a locally convex Hausdorff space (briefly, lcHs) and L(X) denote the space of all continuous linear operators of X into itself. The space L(X) is denoted by Ls(X) when it is equipped with the topology of pointwise convergence in X (i.e. the strong operator topology). By a spectral measure in X is meant a σ-additive map P : Σ → Ls(X), defined on a σ-algebra Σ of subsets of some set Ω, w...

Banach module valued separating maps and automatic continuity

For two algebras $A$ and $B$, a linear map $T:A longrightarrow B$ is called separating, if $xcdot y=0$ implies $Txcdot Ty=0$ for all $x,yin A$. The general form and the automatic continuity of separating maps between various Banach algebras have been studied extensively. In this paper, we first extend the notion of separating map for module case and then we give a description of a linear se...

Automatic Continuity of Homomorphisms Between Banach algebras and Frechet algebras

Double Derivations, Higher Double Derivations and Automatic Continuity

Let  be a Banach algebra. Let  be linear mappings on . First we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple Banach algebras, in certain case. Afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...

On Hölder-continuity of Oseledets subspaces

For Hölder cocycles over a Lipschitz base transformation, possibly noninvertible, we show that the subbundles given by the Oseledets Theorem are Höldercontinuous on compact sets of measure arbitrarily close to 1. The results extend to vector bundle automorphisms, as well as to the Kontsevich-Zorich cocycle over the Teichmüller flow on the moduli space of abelian differentials. Following a recen...