Search results for "Model theory"
showing 10 items of 681 documents
Optimal Extensions of Conformal Mappings from the Unit Disk to Cardioid-Type Domains
2019
AbstractThe conformal mapping $$f(z)=(z+1)^2 $$ f ( z ) = ( z + 1 ) 2 from $${\mathbb {D}}$$ D onto the standard cardioid has a homeomorphic extension of finite distortion to entire $${\mathbb {R}}^2 .$$ R 2 . We study the optimal regularity of such extensions, in terms of the integrability degree of the distortion and of the derivatives, and these for the inverse. We generalize all outcomes to the case of conformal mappings from $${\mathbb {D}}$$ D onto cardioid-type domains.
Qualification conditions for multivalued functions in Banach spaces with applications to nonsmooth vector optimization problems
1994
In this paper we introduce qualification conditions for multivalued functions in Banach spaces involving the A-approximate subdifferential, and we show that these conditions guarantee metric regularity of multivalued functions. The results are then applied for deriving Lagrange multipliers of Fritz—John type and Kuhn—Tucker type for infinite non-smooth vector optimization problems.
Noncommutative Davis type decompositions and applications
2018
We prove the noncommutative Davis decomposition for the column Hardy space $\H_p^c$ for all $0<p\leq 1$. A new feature of our Davis decomposition is a simultaneous control of $\H_1^c$ and $\H_q^c$ norms for any noncommutative martingale in $\H_1^c \cap \H_q^c$ when $q\geq 2$. As applications, we show that the Burkholder/Rosenthal inequality holds for bounded martingales in a noncommutative symmetric space associated with a function space $E$ that is either an interpolation of the couple $(L_p, L_2)$ for some $1<p<2$ or is an interpolation of the couple $(L_2, L_q)$ for some $2<q<\infty$. We also obtain the corresponding $\Phi$-moment Burkholder/Rosenthal inequality for Orlicz functions that…
Weyl-Type Theorems on Banach Spaces Under Compact Perturbations
2018
In this paper, we study Browder-type and Weyl-type theorems for operators $$T+K$$ defined on a Banach space X, where K is (a non necessarily commuting) compact operator on X. In the last part, the theory is exemplified in the case of isometries, analytic Toeplitz operators, semi-shift operators, and weighted right shifts.
Fractional Hardy-Sobolev type inequalities for half spaces and John domains
2018
As our main result we prove a variant of the fractional Hardy-Sobolev-Maz'ya inequality for half spaces. This result contains a complete answer to a recent open question by Musina and Nazarov. In the proof we apply a new version of the fractional Hardy-Sobolev inequality that we establish also for more general unbounded John domains than half spaces.
New results concerning Chebyshev–Grüss-type inequalities via discrete oscillations
2014
The classical form of Gruss' inequality was first published by G. Gruss and gives an estimate of the difference between the integral of the product and the product of the integrals of two functions. In the subsequent years, many variants of this inequality appeared in the literature. The aim of this paper is to consider some new bivariate Chebyshev-Gruss-type inequalities via discrete oscillations and to apply them to different tensor products of linear (not necessarily) positive, well-known operators. We also compare the new inequalities with some older results. In the end we give a Chebyshev-Gruss-type inequality with discrete oscillations for more than two functions.
Some kind of Bishop-Phelps-Bollobás property
2016
In this paper we introduce two Bishop–Phelps–Bollobas type properties for bounded linear operators between two Banach spaces X and Y: property 1 and property 2. These properties are motivated by a Kim–Lee result which states, under our notation, that a Banach space X is uniformly convex if and only if the pair (X,K) satisfies property 2. Positive results of pairs of Banach spaces (X,Y) satisfying property 1 are given and concrete pairs of Banach spaces (X,Y) failing both properties are exhibited. A complete characterization of property 1 for the pairs (lp,lq) is also provided.
Browder-Type Theorems
2018
This chapter may be viewed as the part of the book in which the interaction between local spectral theory and Fredholm theory comes into focus. The greater part of the chapter addresses some classes of operators on Banach spaces that have a very special spectral structure. We have seen that the Weyl spectrum σw(T) is a subset of the Browder spectrum σb(T) and this inclusion may be proper. In this chapter we investigate the class of operators on complex infinite-dimensional Banach spaces for which the Weyl spectrum and the Browder spectrum coincide. These operators are said to satisfy Browder’s theorem. The operators which satisfy Browder’s theorem have a very special spectral structure, ind…
Weyl-Type Theorems
2018
In the previous chapters we introduced several classes of operators which have their origin in Fredholm theory. We also know that the spectrum of a bounded linear operator T on a Banach space X can be split into subsets in many different ways.
Decompositions and asymptotic limit for bicontractions
2012
The asymptotic limit of a bicontraction T (that is, a pair of commuting contractions) on a Hilbert space H is used to describe a Nagy–Foias–Langer type decomposition of T. This decomposition is refined in the case when the asymptotic limit of T is an orthogonal projection. The case of a bicontraction T consisting of hyponormal (even quasinormal) contractions is also considered, where we have ST∗=S2T∗.