Property (gb) through local spectral theory

Property (gb) for a bounded linear operator T on a Banach space X means that the points c of the approximate point spectrum for which c I-T is upper semi B-Weyl are exactly the poles of the resolvent. In this paper we shall give several characterizations of property (gb). These characterizations are obtained by using typical tools from local spectral theory. We also show that property (gb) holds for large classes of operators and prove the stability of property (gb) under some commuting perturbations

SVEP and local spectral radius formula for unbounded operators

In this paper we study the localized single valued extension property for an unbounded operator T. Moreover, we provide sufficient conditions for which the formula of the local spectral radius holds for these operators

Equivalence after extension and Schur coupling do not coincide on essentially incomparable Banach spaces

In 1994, H. Bart and V. É. Tsekanovskii posed the question whether the Banach space operator relations matricial coupling (MC), equivalence after extension (EAE) and Schur coupling (SC) coincide, leaving only the implication EAE/MC => SC open. Despite several affirmative results, in this paper we show that the answer in general is no. This follows from a complete description of EAE and SC for the case that the operators act on essentially incomparable Banach spaces, which also leads to a new characterisation of the notion of essential incomparability. Concretely, the forward shift operators $U$ on $\ell$$^p$ and $V$ on $\ell$$^p$, for $1 ≤ p, q ≤ \infty, p ≠ q$, are EAE but not SC. As a corollary, SC is not transitive. Under mild assumptions, given $U$ and $V$ that are Atkinson or generalised invertible and EAE, we give a concrete operator $W$ that is SC to both $U$ and $V$, even if $U$ and $V$ are not SC themselves. Some further affirmative results for the case where the Banach spaces are isomorphic are also obtained

Cotauberian Operators on L1(0, 1) Obtained by Lifting

ABSTRACT:We show that the set Td(L1(0, 1)) of cotauberian operators acting on L1(0, 1) is not open, and T ? Td(L1(0, 1)) does not imply T** cotauberian. As a consequence, we derive that the set T(L8(0, 1)) of tauberian operators acting on L8(0, 1) is not open, and that T ? T(L8(0,1)) does not imply T** tauberian

The evaluation of a continuing professional development package for primary care dentists designed to reduce stress, build resilience and improve clinical decision-making

Introduction: Stress and burnout are widely accepted as a problem for primary care dental practitioners. Previous programmes to address this issue have met with some success. Burnout is associated with poor coping skills and emotion regulation, and increased rates of clinical errors. Anxiety is associated with poor decision-making and is thought to be associated with poor clinical decision-making. Attempts to improve decision-making use increasing meta-awareness and review of thinking processes. Bibliotherapy is an effective method of delivering cognitive behavioural therapy as self-help or guided self-help (with some therapist input) formats. Objective: To evaluate the efficacy of a specially designed CPD package which was designed to improve coping skills, build resilience and reduce the impact of anxiety on dentists’ clinical decision-making. Design: A multi-centred quasi-experiment Setting: Lincolnshire and Nottinghamshire (England) 2014 Materials and methods: Thirty-five volunteer primary care dentists used two versions (self-help [SH] and guided self-help [GSH], which included a 3 hour workshop) of a specially written cognitive-behavioural-therapy bibliotherapy programme designed to improve well-being and decision-making. Main Outcome Measures: The main outcome measures were dentists’ burnout, depression, anxiety, stress and decision-making style. Data were also collected on use and evaluation of the programme. Results: At 6 weeks there was a clinically and statistically significant reduction in depression, anxiety and stress levels, a statistically significant reduction in burnout (emotional exhaustion) and hypervigilant decision-making and an increase in personal achievement (burnout). The improvements in depression, stress, emotional exhaustion and hypervigilant decision-making were maintained at 6 months. Dentists were overwhelmingly positive in their evaluation of the project and used most of its contents. Conclusion: With the caveat of small numbers and the lack of a no-treatment control, this project demonstrated that a self-help package can be highly acceptable to dentists and, in the short-to-medium term, improve dentists’ well-being and decision-making with implications for patient safety

Weyl-Type Theorems on Banach Spaces Under Compact Perturbations

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

Some Remarks on the Spectral Properties of Toeplitz Operators

In this paper, we study some local spectral properties of Toeplitz operators T-phi defined on Hardy spaces, as the localized single-valued extension property and the property of being hereditarily polaroid