mathematical field of functional analysis, the Eberlein–Šmulian theorem (named after William Frederick Eberlein and Witold Lwowitsch Schmulian) is a result...

is attached to the Eberlein–Šmulian theorem in functional analysis and the Eberlein compacta in topology. William Frederick Eberlein at the Mathematics...

closed subsets). Bishop–Phelps theorem Banach–Mazur theorem Delta-compactness theorem Dixmier–Ng theorem Eberlein–Šmulian theorem – Relates three different...

Dunford–Schwartz theorem (functional analysis) Eberlein–Šmulian theorem (functional analysis) Goldstine theorem (functional analysis) Hahn–Banach theorem (functional...

Banach–Alaoglu theorem – Theorem in functional analysis Bishop–Phelps theorem Dual norm – Measurement on a normed vector space Eberlein–Šmulian theorem – Relates...

case of the Eberlein–Šmulian theorem. Any general property of Banach spaces continues to hold for Hilbert spaces. The open mapping theorem states that...

mathematician known for his work in functional analysis. The Eberlein–Šmulian theorem and Krein–Smulian theorem are named after him. Kreĭn, M.G. (1965). "Vitolʹd...

spaces. Banach–Alaoglu theorem – Theorem in functional analysis Dual norm – Measurement on a normed vector space Eberlein–Šmulian theorem – Relates three different...

U} as desired. Banach–Alaoglu theorem – Theorem in functional analysis Bishop–Phelps theorem Eberlein–Šmulian theorem – Relates three different kinds...

general, one can characterize weak compactness using sequences. Eberlein–Šmulian theorem—A set A {\displaystyle A} in a Banach space is relatively weakly...

Theorem V.4.2, p. 135. Since weak compactness and weak sequential compactness coincide by the Eberlein–Šmulian theorem. Diestel 1984, p. 6. Theorem 1...

y_{k}-x\rVert \to 0} . Banach–Alaoglu theorem – Theorem in functional analysis Bishop–Phelps theorem Eberlein–Šmulian theorem – Relates three different kinds...

is a Grothendieck space. Conversely, it is a consequence of the Eberlein–Šmulian theorem that a separable Grothendieck space X {\displaystyle X} must be...