منابع مشابه
On Multivalued Cosine Families
Let K be a convex cone in a real Banach space. The main purpose of this paper is to show that for a regular cosine family {Ft : t ∈ R} of linear continuous multifunctions Ft : K → cc(X) there exists a linear continuous multifunction H : K → cc(K) such that Ft(x) ⊂ ∞ X n=0 t (2n)! H(x). Let X be a real normed vector space. We will denote by n(X) the family of all nonempty subsets of X and by cc(...
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A classic result, in its early form due to Cox [2], states that if A is a normed algebra with a unity denoted by 1 and a is an element of A such that supn∈N ‖a− 1‖ < 1, then a = 1. Cox’s version concerned the case of square matrices of a given size. This was later extended to bounded operators on Hilbert space by Nakamura and Yoshida [6], and to an arbitrary normed algebra by Hirschfeld [4] and...
متن کاملZero-two law for cosine families
For (C(t))t≥0 being a strongly continuous cosine family on a Banach space, we show that the estimate lim supt→0+ ‖C(t) − I‖ < 2 implies that C(t) converges to I in the operator norm. This implication has become known as the zero-two law. We further prove that the stronger assumption of supt≥0 ‖C(t) − I‖ < 2 yields that C(t) = I for all t ≥ 0. For discrete cosine families, the assumption supn∈N ...
متن کاملCosine Families and Semigroups Really Dif- fer
We reveal three surprising properties of cosine families, distinguishing them from semigroups of operators: (1) A single trajectory of a cosine family is either strongly continuous or not measurable. (2) Pointwise convergence of a sequence of equibounded cosine families implies that the convergence is almost uniform for time in the entire real line; in particular, cosine families cannot be pert...
متن کاملMultivalued Knowledge-Base based on multivalued Datalog
The basic aim of our study is to give a possible model for handling uncertain information. This model is worked out in the framework of DATALOG. The concept of multivalued knowledgebase will be defined as a quadruple of any background knowledge; a deduction mechanism; a connecting algorithm, and a function set of the program, which help us to determine the uncertainty levels of the results. At ...
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ژورنال
عنوان ژورنال: Journal of Applied Analysis
سال: 2007
ISSN: 1425-6908,1869-6082
DOI: 10.1515/jaa.2007.57