Strictly Singular, Non-compact Operators Exist on the Space of Gowers and Maurey

نویسنده

  • G. ANDROULAKIS
چکیده

We construct a strictly singular non-compact operator on Gowers’ and Maurey’s space GM .

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Class of Banach Spaces with Few Non Strictly Singular Operators

The original motivation for this paper is based on the natural question left open by the Gowers-Maurey solution of the unconditional basic sequence problem for Banach spaces ([12]). Recall that Gowers and Maurey have constructed a Banach space X with a Schauder basis (en)n but with no unconditional basic sequence. Thus, while every infinite dimensional Banach space contains a sequence (xn)n whi...

متن کامل

Maximal Ideals in the Algebra of Operators on Certain Banach Spaces

For a Banach space X, let B(X) denote the Banach algebra of all continuous linear operators on X. First, we study the lattice of closed ideals in B(Jp), where 1 < p < ∞ and Jp is the pth James space. Our main result is that the ideal of weakly compact operators is the unique maximal ideal in B(Jp). Applications of this result include the following. (i) The Brown–McCoy radical of B(X), which by ...

متن کامل

There 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 کامل

Composition operators between growth spaces‎ ‎on circular and strictly convex domains in complex Banach spaces‎

‎Let $\Omega_X$ be a bounded‎, ‎circular and strictly convex domain in a complex Banach space $X$‎, ‎and $\mathcal{H}(\Omega_X)$ be the space of all holomorphic functions from $\Omega_X$ to $\mathbb{C}$‎. ‎The growth space $\mathcal{A}^\nu(\Omega_X)$ consists of all $f\in\mathcal{H}(\Omega_X)$‎ ‎such that $$|f(x)|\leqslant C \nu(r_{\Omega_X}(x)),\quad x\in \Omega_X,$$‎ ‎for some constant $C>0$‎...

متن کامل

Strictly 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 کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2001