Quasi-sectorial contractions
نویسنده
چکیده
We revise the notion of the quasi-sectorial contractions. Our main theorem establishes a relation between semigroups of quasi-sectorial contractions and a class of m−sectorial generators. We discuss a relevance of this kind of contractions to the theory of operator-norm approximations of strongly continuous semigroups.
منابع مشابه
Numerical Range and Quasi - Sectorial Contractions
We apply a method developed by one of the authors, see [1], to localize the numerical range of quasi-sectorial contractions semigroups. Our main theorem establishes a relation between the numerical range of quasi-sectorial contraction semigroups {exp(−tS)}t≥0, and the maximal sectorial generators S. We also give a new prove of the rate O(1/n) for the operator-norm Euler formula approximation: e...
متن کاملOperator Holes and Extensions of Sectorial Operators and Dual Pairs of Contractions
A description of the set of m-sectorial extensions of a dual pair {A1, A2} of nonnegative operators is obtained. Some classes of nonaccretive extensions of the dual pair {A1, A2} are described too. Both problems are reduced to similar problems for a dual pair {T1, T2} of nondensely defined symmetric contractions Tj = (I−Aj)(I+Aj), j ∈ {1, 2}. In turn these problems are reduced to the investigat...
متن کاملFixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications
In this paper, we introduce the concept of generalized quasi-contractions in the setting of cone $b$-metric spaces over Banach algebras. By omitting the assumption of normality we establish common fixed point theorems for the generalized quasi-contractions with the spectral radius $r(lambda)$ of the quasi-contractive constant vector $lambda$ satisfying $r(lambda)in [0,frac{1}{s})$ in the set...
متن کاملFixed points of weak $psi$-quasi contractions in generalized metric spaces
In this paper, we introduce the notion of weak $psi$-quasi contraction in generalized metric spaces and using this notion we obtain conditions for the existence of fixed points of a self map in $D$-complete generalized metric spaces. We deduce some corollaries from our result and provide examples in support of our main result.
متن کاملOn the Lp-theory of C0-semigroups associated with second order elliptic operators. I
We study Lp-theory of second order elliptic divergence type operators with measurable coefficients. To this end, we introduce a new method of constructing positive C0-semigroups on Lp associated with sesquilinear (not necessarily sectorial) forms in L2. A precise condition ensuring that the elliptic operator is associated with a quasi-contractive C0-semigroup on Lp is established.
متن کامل