Contractivity and complete contractivity for finite dimensional Banach spaces
نویسندگان
چکیده
منابع مشابه
On Quasi-contractivity of C0-semigroups on Banach Spaces
A basic result in semigroup theory states that every C0-semigroup is quasi-contractive with respect to some appropriately chosen equivalent norm. This paper contains a counterpart of this well-known fact. Namely, by examining the convergence of the Trotter-type formula (e t n P ) (where P denotes a bounded projection), we prove that whenever the generator A is unbounded it is possible to introd...
متن کاملContractivity of linear fractional transformations
One possible approach to exact real arithmetic is to use linear fractional transformations (LFT's) to represent real numbers and computations on real numbers. Recursive expressions built from LFT's are only convergent (i.e., denote a well-deened real number) if the involved LFT's are suuciently contractive. In this paper, we deene a notion of contrac-tivity for LFT's. It is used for convergence...
متن کاملContractivity of Three Dimensional Shift Radix Systems with Finiteness Property
Let d ≥ 1 be an integer and r = (r1, . . . , rd) ∈ R . We define the shift radix system τr : Z → Z by τr(a) = (a2, . . . , ad,−⌊ra⌋) (a = (a1, . . . , ad)). The shift radix system τr has the finiteness property if each a ∈ Z is eventually mapped to 0 under iterations of τr. The mapping τr can be written as τr(a) = R(r)a + v(a) where R(r) is a d × d matrix and v is a correction term. It has been...
متن کاملContractivity of fractal transforms for image coding
Indexing terms: Coding, Image processing, Fractal transforms In this letter the contractivity of existing fractal transforms for use in image compression schemes is examined. The coding process is described as nonlinear transformation in the finite dimensional euclidean vector space. We derive sufficient conditions for contractivity based on the spectral norm and the spectral radius of the tran...
متن کاملOn the Contractivity of Privacy Mechanisms
We present a novel way to compare the statistical cost of privacy mechanisms using their Dobrushin coefficient. Specifically, we provide upper and lower bounds for the Dobrushin coefficient of a privacy mechanism in terms of its maximal leakage and local differential privacy guarantees. Given the geometric nature of the Dobrushin coefficient, this approach provides some insights into the genera...
متن کاملذخیره 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: Journal of Operator Theory
سال: 2019
ISSN: 0379-4024,1841-7744
DOI: 10.7900/jot.2018jun13.2225