What is... a Hereditarily Indecomposable Banach Space?
نویسندگان
چکیده
منابع مشابه
A Hereditarily Indecomposable Asymptotic `2 Banach Space
A famous open problem in functional analysis is whether there exists a Banach space X such that every (bounded linear) operator on X has the form λ+K where λ is a scalar and K denotes a compact operator. This problem is usually called the “scalar-plus-compact” problem [14]. One of the reasons this problem has become so attractive is that by a result of N. Aronszajn and K.T. Smith [7], if a Bana...
متن کاملInterpolating Hereditarily Indecomposable Banach Spaces
A Banach space X is said to be Hereditarily Indecomposable (H.I.) if for any pair of closed subspaces Y , Z of X with Y ∩ Z = {0}, Y + Z is not a closed subspace. (Throughout this section by the term “subspace” we mean a closed infinite-dimensional subspace of X .) The H.I. spaces form a new and, as we believe, fundamental class of Banach spaces. The celebrated example of a Banach space with no...
متن کاملStrictly Singular Non-compact Operators on Hereditarily Indecomposable Banach Spaces
An example is given of a strictly singular non-compact operator on a Hereditarily Indecomposable, reflexive, asymptotic `1 Banach space. The construction of this operator relies on the existence of transfinite c0-spreading models in the dual of the space.
متن کاملm at h . FA ] 3 1 Ja n 20 06 A HEREDITARILY INDECOMPOSABLE ASYMPTOTIC l 2 BANACH SPACE
A Hereditarily Indecomposable asymptotic ℓ 2 Banach space is constructed. The existence of such a space answers a question of B. Maurey and verifies a conjecture of W.T. Gowers.
متن کاملThere Is No Bound on Sizes of Indecomposable Banach Spaces
Assuming the generalized continuum hypothesis we construct arbitrarily big indecomposable Banach spaces. i.e., such that whenever they are decomposed as X ⊕ Y , then one of the closed subspaces X or Y must be finite dimensional. It requires alternative techniques compared to those which were initiated by Gowers and Maurey or Argyros with the coauthors. This is because hereditarily indecomposabl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Notices of the American Mathematical Society
سال: 2019
ISSN: 0002-9920,1088-9477
DOI: 10.1090/noti1962