v 1 [ m at h . FA ] 1 5 A ug 2 00 0 Representations of Cuntz algebras , loop groups and wavelets Palle
نویسندگان
چکیده
A theorem of Glimm states that representation theory of an NGCR C∗-algebra is always intractable, and the Cuntz algebra ON is a case in point. The equivalence classes of irreducible representations under unitary equivalence cannot be captured with a Borel cross section. Nonetheless, we prove here that wavelet representations correspond to equivalence classes of irreducible representations of ON , and they are effectively labeled by elements of the loop group, i.e., the group of measurable functions A : T → UN (C). These representations of ON are constructed here from an orbit picture analysis of the infinite-dimensional loop group.
منابع مشابه
Closed subspaces which are attractors for representations of the Cuntz algebras
We analyze the structure of co-invariant subspaces for representations of the Cuntz algebras ON for N = 2, 3, . . . , N < ∞, with special attention to the representations which are associated to orthonormal and tight-frame wavelets in L (R) corresponding to scale number N .
متن کاملUse of operator algebras in the analysis of measures from wavelets and iterated function systems
In this paper, we show how a class of operators used in the analysis of measures from wavelets and iterated function systems may be understood from a special family of representations of Cuntz algebras. Let (X, d) be a compact metric space, and let an iterated function system (IFS) be given on X, i.e., a finite set of continuous maps σi: X → X, i = 0, 1, · · · , N −1. The maps σi transform the ...
متن کاملar X iv : 0 90 5 . 08 78 v 1 [ m at h . FA ] 6 M ay 2 00 9 Spectral Models for Orthonormal Wavelets and Multiresolution Analysis of L 2 ( R )
Spectral representations of the dilation and translation operators on L 2 (R) are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions defined on the functional spectral spaces. The approach is useful for computational purposes.
متن کاملar X iv : f un ct - a n / 96 12 00 2 v 1 1 7 D ec 1 99 6 ITERATED FUNCTION SYSTEMS AND PERMUTATION REPRESENTATIONS OF THE CUNTZ ALGEBRA
We study a class of representations of the Cuntz algebras O N , N = 2, 3,. .. , acting on L 2 (T) where T = R2πZ. The representations arise in wavelet theory, but are of independent interest. We find and describe the decomposition into irreducibles, and show how the O N-irreducibles decompose when restricted to the subalgebra UHF N ⊂ O N of gauge-invariant elements; and we show that the whole s...
متن کاملar X iv : m at h / 05 01 13 9 v 2 [ m at h . FA ] 1 A ug 2 00 5 Stability of Adjointable Mappings in Hilbert C ∗ - Modules ∗
The generalized Hyers–Ulam–Rassias stability of adjointable mappings on Hilbert C∗-modules is investigated. As a corollary, we establish the stability of the equation f(x)∗y = xg(y)∗ in the context of C∗-algebras.
متن کامل