Sentence examples for linear derivation from inspiring English sources

Since semisimple algebras are semiprime [18], Theorem 2.2 guarantees that δ is an approximate linear derivation.

We also establish the functional inequalities related to a linear derivation and their stability.

Then we examine the functional inequalities related to a linear derivation and their stability.

Singer and Wermer [20] proved that if is a commutative Banach algebra and is a continuous linear derivation, then They also conjectured that the same result holds even is a discontinuous linear derivation.

The Singer-Wermer conjecture implies that any linear derivation on a commutative semisimple Banach algebra is identically zero [11].

Then is a linear generalized left derivation and is a linear derivation which maps into the intersection of the center and the Jacobson radical of.

Hence linear derivations on Banach algebras (if everywhere defined) genuinely belong to the noncommutative setting.

We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.

Singer and Wermer in [9] obtained a fundamental result which started investigation into the ranges of linear derivations on Banach algebras.

In particular, mappings satisfying such functional inequalities on a semiprime Banach algebra are linear derivations which map into the intersection of the center and the radical.

As a direct consequence, we see that there are no nonzero linear derivations on a semisimple commutative Banach algebra, which had been proved by Johnson [22].