Wyniki wyszukiwania

1

Rotundity and smoothness of convex bodies in reflexive and nonreflexive spaces

100%

Klee V., Veselý L., Zanco C.

Studia Mathematica

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1996

|

tom 120

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nr 3

191-204

EN

For combining two convex bodies C and D to produce a third body, two of the most important ways are the operation ∓ of forming the closure of the vector sum C+D and the operation γ̅ of forming the closure of the convex hull of C ⋃ D. When the containing normed linear space X is reflexive, it follows from weak compactness that the vector sum and the convex hull are already closed, and from this it follows that the class of all rotund bodies in X is stable with respect to the operation ∓ and the class of all smooth bodies in X is stable with respect to both ∓ and γ̅. In our paper it is shown that when X is separable, these stability properties of rotundity (resp. smoothness) are actually equivalent to the reflexivity of X. The characterizations remain valid for each nonseparable X that contains a rotund (resp. smooth) body.

2

Correction to "Summability in $ł(p_{1},p_{2},...)$ spaces" Studia Mathematica 25 (1965), p. 277-280)

98%

Klee V.

Studia Mathematica

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1969

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tom 33

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nr 3

345

3

Tiling with smooth and rotund tiles

75%

Klee V., Maluta E., Zanco C.

Fundamenta Mathematicae

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1985-1986

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tom 126

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nr 3

269-290

4

Mappings into normed linear spaces

62%

Klee V.

Fundamenta Mathematicae

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1960-1961

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tom 49

|

nr 1

25-34

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Studia Mathematica

4 Klee V.

2 Zanco C.

1 Maluta E.

1 Veselý L.

1 1996

1 1986

1 1969

1 1960

Rotundity and smoothness of convex bodies in reflexive and nonreflexive spaces

Correction to "Summability in $ł(p_{1},p_{2},...)$ spaces" Studia Mathematica 25 (1965), p. 277-280)

Tiling with smooth and rotund tiles

Mappings into normed linear spaces