Local Automorphisms of the Unitary Group and the General Linear Group on a Hilbert Space
نویسنده
چکیده
We prove that every 2-local automorphism of the unitary group or the general linear group on a complex infinite-dimensional separable Hilbert space is an automorphism. Thus these types of transformations are completely determined by their local actions on the two-points subsets of the groups in question.
منابع مشابه
On C0-Group of Linear Operators
In this paper we consider C0-group of unitary operators on a Hilbert C*-module E. In particular we show that if A?L(E) be a C*-algebra including K(E) and ?t a C0-group of *-automorphisms on A, such that there is x?E with =1 and ?t (?x,x) = ?x,x t?R, then there is a C0-group ut of unitaries in L(E) such that ?t(a) = ut a ut*.
متن کاملOD-characterization of $U_3(9)$ and its group of automorphisms
Let $L = U_3(9)$ be the simple projective unitary group in dimension 3 over a field with 92 elements. In this article, we classify groups with the same order and degree pattern as an almost simple group related to $L$. Since $Aut(L)equiv Z_4$ hence almost simple groups related to $L$ are $L$, $L : 2$ or $L : 4$. In fact, we prove that $L$, $L : 2$ and $L : 4$ are OD-characterizable.
متن کاملMulti-Frame Vectors for Unitary Systems in Hilbert $C^{*}$-modules
In this paper, we focus on the structured multi-frame vectors in Hilbert $C^*$-modules. More precisely, it will be shown that the set of all complete multi-frame vectors for a unitary system can be parameterized by the set of all surjective operators, in the local commutant. Similar results hold for the set of all complete wandering vectors and complete multi-Riesz vectors, when the surjective ...
متن کاملCoherent Frames
Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) on a single element $f$ in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space $mathcal{H}$ which is indexed by some locally compact group $G$, equipped with its left Haar measure. These frames are obtained as the orbits of ...
متن کاملAlgebraic Reflexivity of Isometry Groups and Automorphism Groups of Some Operator Structures
We establish the algebraic reflexivity of three isometry groups of operator structures: The group of all surjective isometries on the unitary group, the group of all surjective isometries on the set of all positive invertible operators equipped with the Thompson metric, and the group of all surjective isometries on the general linear group of B(H), the operator algebra over a complex infinite d...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008