On Stability and Weak-Star Stability of $$\varepsilon $$-Isometries

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Xiaoling Chen ◽  
Lixin Cheng ◽  
Wen Zhang
Keyword(s):  
Weak Star

Bergman Spaces on Disconnected Domains

1996 ◽  
Vol 48 (2) ◽  
pp. 225-243
Author(s):  
Alexandru Aleman ◽  
Stefan Richter ◽  
William T. Ross
Keyword(s):  
Measure Zero ◽  
Bergman Spaces ◽  
Dirichlet Space ◽  
Invariant Subspaces ◽  
Compact Set ◽  
Bounded Region ◽  
Area Measure ◽  
Weak Star ◽  
Harmonic Dirichlet Space ◽  
Disconnected Domains

AbstractFor a bounded region G ⊂ ℂ and a compact set K ⊂ G, with area measure zero, we will characterize the invariant subspaces ℳ (under ƒ → zƒ) of the Bergman space (G \ K), 1 ≤ p < ∞, which contain (G) and with dim(ℳ/(z - λ)ℳ) = 1 for all λ ∈ G \ K. When G \ K is connected, we will see that dim(ℳ/(z - λ)ℳ) = 1 for all λ ∈ G \ K and thus in this case we will have a complete description of the invariant subspaces lying between (G) and (G \ K). When p = ∞, we will remark on the structure of the weak-star closed z-invariant subspaces between H∞(G) and H∞(G \ K). When G \ K is not connected, we will show that in general the invariant subspaces between (G) and (G \ K) are fantastically complicated. As an application of these results, we will remark on the complexity of the invariant subspaces (under ƒ → ζƒ) of certain Besov spaces on K. In particular, we shall see that in the harmonic Dirichlet space , there are invariant subspaces ℱ such that the dimension of ζℱ in ℱ is infinite.

Weak-Star Continuous Analytic Functions

1995 ◽  
Vol 47 (4) ◽  
pp. 673-683 ◽  
Author(s):  
R. M. Aron ◽  
B. J. Cole ◽  
T. W. Gamelin
Keyword(s):  
Unit Ball ◽  
Finite Type ◽  
Analytic Functions ◽  
Approximation Property ◽  
Entire Functions ◽  
Open Unit ◽  
Closed Unit Ball ◽  
Open Unit Ball ◽  
Weakly Continuous ◽  
Weak Star

AbstractLet 𝒳 be a complex Banach space, with open unit ball B. We consider the algebra of analytic functions on B that are weakly continuous and that are uniformly continuous with respect to the norm. We show these are precisely the analytic functions on B that extend to be weak-star continuous on the closed unit ball of 𝒳**. If 𝒳* has the approximation property, then any such function is approximable uniformly on B by finite polynomials in elements of 𝒳*. On the other hand, there exist Banach spaces for which these finite-type polynomials fail to approximate. We consider also the approximation of entire functions by finite-type polynomials. Assuming 𝒳* has the approximation property, we show that entire functions are approximable uniformly on bounded sets if and only if the spectrum of the algebra of entire functions coincides (as a point set) with 𝒳**.

scholarly journals Magnetism of the He-weak star HR 2949

2010 ◽  
Vol 6 (S272) ◽  
pp. 210-211
Author(s):  
Thomas Rivinius ◽  
Gregg A. Wade ◽  
Richard H. D. Townsend ◽  
Matthew Shultz ◽  
Jason H. Grunhut ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Line Profile ◽  
Equivalent Width ◽  
Rotational Line ◽  
Phase Lag ◽  
Abundance Patterns ◽  
Weak Star ◽  
Hydrogen Lines

AbstractA magnetic field and rotational line profile variability (lpv) is found in the He-weak star HR 2949. The field measured from metallic lines varies in a clearly non-sinusoidal way, and shows a phase lag relative to the morphologically similar He i equivalent width variations. The surface abundance patterns are strong and complex, and visible even in the hydrogen lines.

scholarly journals Dual Algebras and A-Measures

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Marek Kosiek ◽  
Krzysztof Rudol
Keyword(s):  
Analytic Functions ◽  
Complete Solution ◽  
Holomorphic Functions ◽  
Classical Case ◽  
Function Algebra ◽  
Domain Of Holomorphy ◽  
Strict Pseudoconvexity ◽  
Weak Star ◽  
Spectrum Of A Function ◽  
Bounded Holomorphic

Weak-star closures of Gleason parts in the spectrum of a function algebra are studied. These closures relate to the bidual algebra and turn out both closed and open subsets of a compact hyperstonean space. Moreover, weak-star closures of the corresponding bands of measures are reducing. Among the applications we have a complete solution of an abstract version of the problem, whether the set of nonnegative A-measures (called also Henkin measures) is closed with respect to the absolute continuity. When applied to the classical case of analytic functions on a domain of holomorphyΩ⊂Cn, our approach avoids the use of integral formulae for analytic functions, strict pseudoconvexity, or some other regularity ofΩ. We also investigate the relation between the algebra of bounded holomorphic functions onΩand its abstract counterpart—thew* closure of a function algebraAin the dual of the band of measures generated by one of Gleason parts of the spectrum ofA.

Uniqueness of Preduals in Spaces of Operators

2014 ◽  
Vol 57 (4) ◽  
pp. 810-813 ◽  
Author(s):  
G. Godefroy
Keyword(s):  
Linear Subspace ◽  
Closed Linear Subspace ◽  
Reflexive Space ◽  
Spaces Of Operators ◽  
Weak Star

AbstractWe show that if E is a separable reflexive space, and L is a weak-star closed linear subspace of L(E) such that L ∩ K(E) is weak-star dense in L, then L has a unique isometric predual. The proof relies on basic topological arguments.

On Quasisimilarity for Subnormal Operators, II

1982 ◽  
Vol 25 (1) ◽  
pp. 37-40 ◽  
Author(s):  
John B. Conway
Keyword(s):  
Subnormal Operator ◽  
Unilateral Shift ◽  
Closed Algebra ◽  
Subnormal Operators ◽  
Weak Star

AbstractLet S be a subnormal operator and let be the weak-star closed algebra generated by S and 1. An example of an irreducible cyclic subnormal operator S is found such that there is a T in with S and T quasisimilar but not unitarily equivalent. However, if S is the unilateral shift, T ∈ and S and T are quasisimilar, then S ≅ T.

Completions of Boolean algebras of projections and weak-star closures of C*-algebras on dual Banach spaces

2011 ◽  
Vol 54 (2) ◽  
pp. 515-529
Author(s):  
Philip G. Spain
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Boolean Algebras ◽  
C Algebra ◽  
C Algebras ◽  
Weak Star ◽  
Weakly Closed ◽  
Operator Closure ◽  
Dual Banach Space ◽  
Completion Theorem

AbstractPalmer has shown that those hermitians in the weak-star operator closure of a commutative C*-algebra represented on a dual Banach space X that are known to commute with the initial C*-algebra form the real part of a weakly closed C*-algebra on X. Relying on a result of Murphy, it is shown in this paper that this last proviso may be dropped, and that the weak-star closure is even a W*-algebra.When the dual Banach space X is separable, one can prove a similar result for C*-equivalent algebras, via a ‘separable patch’ completion theorem for Boolean algebras of projections on such spaces.

scholarly journals The accelerating rotation of the magnetic He-weak star HD 142990

2019 ◽  
Vol 486 (4) ◽  
pp. 5558-5566 ◽  
Author(s):  
M Shultz ◽  
Th Rivinius ◽  
B Das ◽  
G A Wade ◽  
P Chandra
Keyword(s):  
Rotation Period ◽  
Photometric Data ◽  
Data Sets ◽  
Surface Magnetic Field ◽  
Short Rotation ◽  
Magnetic Stars ◽  
Weak Star ◽  
Rotational Evolution ◽  
Strong Surface ◽  
Rapid Rotator

ABSTRACT HD 142990 (V 913 Sco; B5 V) is a He-weak star with a strong surface magnetic field and a short rotation period (Prot ∼ 1 d). Whilst it is clearly a rapid rotator, recent determinations of Prot are in formal disagreement. In this paper, we collect magnetic and photometric data with a combined 40-yr baseline in order to re-evaluate Prot and examine its stability. Both period analysis of individual data sets and O − C analysis of the photometric data demonstrate that Prot has decreased over the past 30 yr, violating expectations from magnetospheric braking models, but consistent with behaviour reported for 2 other hot, rapidly rotating magnetic stars, CU Vir and HD 37776. The available magnetic and photometric time series for HD 142990 can be coherently phased assuming a spin-up rate $\dot{P}$ of approximately −0.6 s yr−1, although there is some indication that $\dot{P}$ may have slowed in recent years, possibly indicating an irregular or cyclic rotational evolution.

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