Every non-smooth 2-dimensional Banach space has the Mazur–Ulam property

نویسندگان

چکیده

A Banach space $X$ has the $Mazur$-$Ulam$ $property$ if any isometry from unit sphere of onto other $Y$ extends to a linear spaces $X,Y$. is called $smooth$ ball unique supporting functional at each point sphere. We prove that non-smooth 2-dimensional Mazur-Ulam property.

برای دانلود باید عضویت طلایی داشته باشید

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Every Banach Space is Reflexive

The title above is wrong, because the strong dual of a Banach space is too strong to assert that the natural correspondence between a space and its bidual is an isomorphism. This, from a categorical point of view, is indeed the right duality concept because it yields a self adjoint dualisation functor. However, for many applications the non–reflexiveness problem can be solved by replacing the n...

متن کامل

Weak Banach-Saks property in the space of compact operators

For suitable Banach spaces $X$ and $Y$ with Schauder decompositions and‎ ‎a suitable closed subspace $mathcal{M}$ of some compact operator space from $X$ to $Y$‎, ‎it is shown that the strong Banach-Saks-ness of all evaluation‎ ‎operators on ${mathcal M}$ is a sufficient condition for the weak‎ ‎Banach-Saks property of ${mathcal M}$, where for each $xin X$ and $y^*in‎ ‎Y^*$‎, ‎the evaluation op...

متن کامل

Non-smooth Analysis, Optimisation Theory and Banach Space Theory

The questions listed here do not necessarily represent the most significant problems from the areas of Non-smooth Analysis, Optimisation theory and Banach space theory, but rather, they represent a selection of problems that are of interest to the authors. 1. Weak Asplund spaces Let X be a Banach space. We say that a function φ : X → R is Gâteaux differentiable at x ∈ X if there exists a contin...

متن کامل

Every Countable Group Has the Weak Rohlin Property

We present a simple proof of the fact that every countable group Γ is weak Rohlin, that is, there is in the Polish space AΓ of measure preserving Γ-actions an action T whose orbit in AΓ under conjugations is dense. In conjunction with earlier results this in turn yields a new characterization of non-Kazhdan groups as those groups which admit such an action T which is also ergodic.

متن کامل

weak banach-saks property in the space of compact operators

for suitable banach spaces $x$ and $y$ with schauder decompositions and‎ ‎a suitable closed subspace $mathcal{m}$ of some compact operator space from $x$ to $y$‎, ‎it is shown that the strong banach-saks-ness of all evaluation‎ ‎operators on ${mathcal m}$ is a sufficient condition for the weak‎ ‎banach-saks property of ${mathcal m}$, where for each $xin x$ and $y^*in‎ ‎y^*$‎, ‎the evaluation op...

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

ژورنال

عنوان ژورنال: Linear Algebra and its Applications

سال: 2021

ISSN: ['1873-1856', '0024-3795']

DOI: https://doi.org/10.1016/j.laa.2021.04.020