A Remark on Closed Noncommutative Subspaces
نویسندگان
چکیده
Given an abelian category with arbitrary products, arbitrary coproducts, and a generator, we show that the closed subspaces (in the sense of A. L. Rosenberg) are parameterized by a suitably defined poset of ideals in the generator. In particular, the collection of closed subspaces is itself a small poset.
منابع مشابه
Weak*-closed invariant subspaces and ideals of semigroup algebras on foundation semigroups
Let S be a locally compact foundation semigroup with identity and be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of In this paper, we prove that X is invariantly complemented in if and only if the left ideal of has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenab...
متن کاملUnitary Invariants in Multivariable Operator Theory
The problems considered in this paper come as a natural continuation of our program to develop a free analogue of Sz.-Nagy–Foiaş theory, for row contractions. An n-tuple (T1, . . . , Tn) of operators acting on a Hilbert space is called row contraction if T1T ∗ 1 + · · ·+ TnT ∗ n ≤ I. In this study, the role of the unilateral shift is played by the left creation operators on the full Fock space ...
متن کاملOn Bilateral Weighted Shifts in Noncommutative Multivariable Operator Theory
We present a generalization of bilateral weighted shift operators for the noncommutative multivariable setting. We discover a notion of periodicity for these shifts, which has an appealing diagramatic interpretation in terms of an infinite tree structure associated with the underlying Hilbert space. These shifts arise naturally through weighted versions of certain representations of the Cuntz C...
متن کاملClosed Projections and Peak Interpolation for Operator Algebras
The closed one-sided ideals of a C-algebra are exactly the closed subspaces supported by the orthogonal complement of a closed projection. Let A be a (not necessarily selfadjoint) subalgebra of a unital C-algebra B which contains the unit of B. Here we characterize the right ideals of A with left contractive approximate identity as those subspaces of A supported by the orthogonal complement of ...
متن کامل6 M ay 2 00 6 Noncommutative Maslov Index and Eta - Forms
We define and prove a noncommutative generalization of a formula relating the Maslov index of a triple of Lagrangian subspaces of a symplectic vector space to eta-invariants associated to a pair of Lagrangian subspaces. The noncommutative Maslov index, defined for modules over a C∗-algebra A, is an element in K0(A). The generalized formula calculates its Chern character in the de Rham homology ...
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 2005