Linear maps determining the norm topology

Let be a Banach function algebra on a compact space , and let be such that for any scalar the element is not a divisor of zero. We show that any complete norm topology on that makes the multiplication by continuous is automatically equivalent to the original norm topology of . Related results for general Banach spaces are also discussed.

     

Biharmonic maps, conformal deformations and the Hopf maps

We consider harmonic semi-conformal maps between two Riemannian manifolds. By deforming conformally the codomain metric, we construct new examples of non-harmonic biharmonic maps.     

Operator norm inequalities in semi-Hilbertian spaces

In this work we extend Cordes inequality, McIntosh inequality and CPR-inequality for the operator seminorm defined by a positive semidefinite bounded linear operator A.     

Lacunary series in mixed norm spaces in the disc

The paper establishes a necessary and sufficient condition under which a lacunary series belong to a mixed norm space of functions holomorphic in the unit disc. As a corollary, some sharp pointwise estimates are obtained for lacunary series.     

Korenblum maximum principle in mixed norm spaces

Archiv der Mathematik - It is well known that the Korenblum maximum principle holds in Bergman spaces $$mathrm {A}^{p}$$ if and only if $$pge 1$$ . In this note, we improve this result by proving...     

Differentiation of inverse functions in spaces without norm

Kazakh State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 27, No. 4, pp. 84–87, October–December, 1993.     

Nonlinear maps in spaces of distributions

This research was started while the author was visiting University of Pisa, University of Ferrara and I.C.T.P., Trieste in the autumn of 1988