Automatic continuity and second order cohomology

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 ...

Automatic Program Synthesis in Second-Order Logic

Abetract A resolution-based theorem prover, incorporating a restricted higher-order unification algorithm , has been applied to the automatic synthesis of SN0B0L-4 programs. The set of premisses includes second-order assignment and iteration axioms derived from those of Hoare. Two examples are given of the synthesis of programs that compute elementary functions. Descriptive Terms Higher-order l...

Second Hochschild Cohomology of Convolution Algebras