Entropy of Absolute Convex Hulls in Hilbert Spaces
نویسنده
چکیده
The metric entropy of absolute convex hulls of sets in Hilbert spaces is studied for the general case when the metric entropy of the sets is arbitrary. Under some regularity assumptions, the results are sharp.
منابع مشابه
Gelfand numbers and metric entropy of convex hulls in Hilbert spaces
We establish optimal estimates of Gelfand numbers or Gelfand widths of absolutely convex hulls cov(K) of precompact subsets K ⊂ H of a Hilbert space H by the metric entropy of the set K where the covering numbers N(K, ") of K by "-balls of H satisfy the Lorentz condition ∫ ∞ 0 ( log2N(K, ") )r/s d" <∞ for some fixed 0 < r, s ≤ ∞ with the usual modifications in the cases r = ∞, 0 < s < ∞ and 0 <...
متن کاملMetric Entropy of Convex Hulls
Let T be a precompact subset of a Hilbert space. The metric entropy of the convex hull of T is estimated in terms of the metric entropy of T , when the latter is of order α = 2. The estimate is best possible. Thus, it answers a question left open in [LL] and [CKP]. 0.
متن کاملA New Quantum f-Divergence for Trace Class Operators in Hilbert Spaces
A new quantum f -divergence for trace class operators in Hilbert Spaces is introduced. It is shown that for normalised convex functions it is nonnegative. Some upper bounds are provided. Applications for some classes of convex functions of interest are also given.
متن کاملMETRIC ENTROPY OF CONVEX HULLS IN TYPE p SPACES—THE CRITICAL CASE
Given a precompact subset A of a type p Banach space E, where p ∈ (1, 2], we prove that for every β ∈ [0, 1) and all n ∈ N sup k≤n k ′ (log k)ek(acoA) ≤ c sup k≤n k ′ (log k)ek(A) holds, where acoA is the absolutely convex hull of A and ek(.) denotes the kth dyadic entropy number. With this inequality we show in particular that for given A and β ∈ (−∞, 1) with en(A) ≤ n−1/p ′ (logn)−β for all n...
متن کاملStrong convergence theorem for a class of multiple-sets split variational inequality problems in Hilbert spaces
In this paper, we introduce a new iterative algorithm for approximating a common solution of certain class of multiple-sets split variational inequality problems. The sequence of the proposed iterative algorithm is proved to converge strongly in Hilbert spaces. As application, we obtain some strong convergence results for some classes of multiple-sets split convex minimization problems.
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 2002