Bounded normal generation and invariant automatic continuity

Automatic Invariant Generation

Program invariants are statements or assertions that are widely used in program analysis and proving correctness of programs. A program invariant can be defined for every program location. Invariants provide properties that hold for every valid program execution, and are crucial in program verification. In this survey, we shall describe some techniques that have been used in the past to generat...

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 Generation of Epsilon-Delta Proofs of Continuity

As part of a project on automatic generation of proofs involving both logic and computation, we have automated the production of some proofs involving epsilon-delta arguments. These proofs involve two or three quantifiers on the logical side, and on the computational side, they involve algebra, trigonometry, and some calculus. At the border of logic and computation, they involve several types o...