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Continuity of generalized inverses in Banach algebras

Steffen Roch, Bernd Silbermann (1999)

Studia Mathematica

The main topic of the paper is the continuity of several kinds of generalized inversion of elements in a Banach algebra with identity. We introduce the notion of asymptotic generalized invertibility and completely characterize sequences of elements with this property. Based on this result, we derive continuity criteria which generalize the well known criteria from operator theory.

Continuity of Pseudo-differential Operators on Bessel And Besov Spaces

Moussai, Madani (2001)

Serdica Mathematical Journal

We study the continuity of pseudo-differential operators on Bessel potential spaces Hs|p (Rn ), and on the corresponding Besov spaces B^(s,q)p (R ^n). The modulus of continuity ω we use is assumed to satisfy j≥0, ∑ [ω(2−j )Ω(2j )]2 < ∞ where Ω is a suitable positive function.

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