##### Venue: LH 3

Having been unclear how to widely define strong (or strict) pseudoconvexity in the infinite-dimensional context, we compared the concept in the smooth-boundary case with strict convexity. As a result, w= e accomplished establishing definitions of local uniform pseudoconvexity, uniform pseudoconvexity and strict pseudoconvexity for open and bounded subsets of a Banach space. We will see examples of Banach spaces with uniformly pseudoconvex unit ball, as well as examples of Banach spaces whose unit ball is not even strictly pseudoconvex. As an application of the techniques developed, we show that in finite dimension the concept of strict plurisubharmonicity coincides with strict plurisubharmonicity in distribution.

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