Subspace gaps and Weyl's theorem for an elementary operator
نویسنده
چکیده
A range-kernal orthogonality property is established for the elementary operators (X) = ∑n i=1AiXBi and ∗(X) = ∑n i=1A ∗ i XB ∗ i , where A = (A1,A2, . . . ,An) and B = (B1,B2, . . . ,Bn) are n-tuples of mutually commuting scalar operators (in the sense of Dunford) in the algebra B(H) of operators on a Hilbert space H . It is proved that the operator satisfies Weyl’s theorem in the case in which A and B are n-tuples of mutually commuting generalized scalar operators.
منابع مشابه
An Elementary Proof of the Restricted Invertibility Theorem *
We give an elementary proof of a generalization of Bourgain and Tzafriri’s Restricted Invertibility Theorem, which says roughly that any matrix with columns of unit length and bounded operator norm has a large coordinate subspace on which it is well-invertible. Our proof gives the tightest known form of this result, is constructive, and provides a deterministic polynomial time algorithm for fin...
متن کاملThe Basic Theorem and its Consequences
Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...
متن کاملAn Lp-Lq-version Of Morgan's Theorem For The Generalized Fourier Transform Associated with a Dunkl Type Operator
The aim of this paper is to prove new quantitative uncertainty principle for the generalized Fourier transform connected with a Dunkl type operator on the real line. More precisely we prove An Lp-Lq-version of Morgan's theorem.
متن کاملEgoroff Theorem for Operator-Valued Measures in Locally Convex Cones
In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...
متن کاملA generalized Weyl equidistribution theorem for operators with applications
The present paper is motivated by the observation that Weyl's equidistribution theorem for real sequences on a bounded interval can be formulated in a way which is also meaningful for sequences of self-adjoint operators on a hilbert space. We shall provide general results on weak convergence of operator measures which yield this version of Weyl's theorem as a corollary. Further, by combining th...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Int. J. Math. Mathematical Sciences
دوره 2005 شماره
صفحات -
تاریخ انتشار 2005