A difference between continuous and absolutely continuous norms in Banach function spaces
On examples we show a difference between a continuous and absolutely continuous norm in Banach function spaces.
Traces of a weighted Sobolev space in a singular case
Zobecněné trigonometrické funkce z různých úhlů pohledu
Explicit representation of compact linear operators in Banach spaces via polar sets
We consider a compact linear map T acting between Banach spaces both of which are uniformly convex and uniformly smooth; it is supposed that T has trivial kernel and range dense in the target space. It is shown that if the Gelfand numbers of T decay sufficiently quickly, then the action of T is given by a series with calculable coefficients. This provides a Banach space version of the well-known Hilbert space result of E. Schmidt.
Series representation of compact linear operators in Banach spaces
Let and ; suppose that is a compact linear map with trivial kernel and range dense in . It is shown that if the Gelfand numbers of decay sufficiently quickly, then the action of is given by a series with calculable coefficients. The special properties of enable this to be established under weaker conditions on the Gelfand numbers than in earlier work set in the context of more general spaces.
Are some optimal shape problems convex?
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