Property (w) and perturbations

A bounded linear operator T ∈ L(X) defined on a Banach space X satisfies property (w), a variant of Weyl’s theorem, if the complement in the approximate point spectrum σa(T ) of the Weyl essential approximate spectrum σwa(T ) coincides with the set of all isolated points of the spectrum which are eigenvalues of finite multiplicity. In this note, we study the stability of property (w), for a bounded operator T acting on a Banach space, under perturbations by finite rank operators, by nilpotent operator and quasi-nilpotent operators commuting with T

Classes of operators satisfying a-Weyl's theorem

In this article Weyl's theorem and a-Weyl's theorem on Banach spaces are related to an important property which has a leading role in local spectral theory: the single-valued extension theory. We show that if T has SVEP then Weyl's theorem and a-Weyl's theorem for T* are equivalent, and analogously, if T* has SVEP then Weyl's theorem and a-Weyl's theorem for T are equivalent. From this result we deduce that a-Weyl's theorem holds for classes of operators for which the quasi-nilpotent part H 0(λI-T) is equal to ker (λI -T)p for some p ∈ ℕ and every λ ∈ ℂ, and for algebraically paranormal operators on Hilbert spaces. We also improve recent results established by Curto and Han, Han and Lee, and Oudghiri

Percutaneous Renal Cryoablation

This research topic discusses how safe and effective the use of cryoablation is to treat a renal tumor. Cryoablation is a procedure performed in the Interventional Radiology department to kill cancer cells using very cold temperatures. This procedure is done when the patient cannot have surgery to remove the tumor itself. Although the tumor is not removed during cryoablation, the treatment is performed to freeze the tumor to prohibit growth while releasing antigens from the tumor which triggers an immune response. To see if cryoablation is as effective as some say, a qualitative study was conducted which used 174 renal tumors that were treated by computed tomography (CT) guided cryoablations done between February of 2011 and June of 2020. Procedural success, effectiveness and complications were evaluated for each procedure. The results of this study were that in 98.3% of tumors (171/174), procedural success was achieved. The effectiveness of treatments was 95.3% which then increased to 98.2% after retreats. Overall, there was a complication rate of 29.8%. At 1 year after the procedure there was 100% recurrence-free survival, at 3 years there was 95.3% recurrence-free survival and at 5 years there was 88.6% recurrence-free survival. From this study one can conclude that cryoablation is a safe and effective procedure even years after it is performed. This technique is able to treat small renal tumors without any major complications. Possible implications from this research could be used while working in the interventional radiology department to ensure patients understand that this procedure is safe and effective. Keywords: cryoablation; renal tumor treatment; renal cryoablation; interventional radiologyhttps://digitalcommons.misericordia.edu/medimg_seniorposters/1021/thumbnail.jp

Meaning In Life As A Moderator Of Resilience And Traumatic Stress: A Study Of Protective Factors And Sex Differences In A Sample Of Mississippi Coastal Residents Seeking Mental Health Services After The Deepwater Horizon Oil Spill

In April of 2010, the Deepwater Horizon oil platform exploded, releasing millions of barrels of crude oil into the Gulf of Mexico, becoming the largest oil spill in U.S. history. Disasters often lead to a decrease in psychological well-being for those affected by the disaster. Positive psychological constructs such as resilience and perceived meaning in life have been shown to be significant protective factors against the negative psychological effects of a disaster. Utilizing a sample of 1119 adults seeking mental health services along the coast of Mississippi after the spill, the current study aimed to investigate the relationship between these protective factors and posttraumatic stress and to investigate if sex moderates the relationship between posttraumatic stress and protective factors. An independent samples t-test determined that there were no significant differences in perceived resilience or perceived meaning between the non-effects and effects groups. An independent samples t-test determined that those who reported an effect from the spill endorsed higher levels of posttraumatic stress. Multiple hierarchical regression analysis determined that after controlling for the impact of the spill in the perceived effects group, resilience and perceived meaning were significant predictors of posttraumatic stress symptoms. Moderation analyses were conducted using the ordinary least squares regression-based method. It was found that meaning in life did not serve as a moderator in the relationship between resilience and posttraumatic stress. An independent samples t-test determined that there were no significant differences in reported levels of posttraumatic stress symptoms between males and females in the effects group. Lastly, it was determined that sex did not moderate the relationship between resilience and posttraumatic stress symptoms or between perceived meaning in life and posttraumatic stress symptoms. Overall, this study further demonstrates the importance of resilience and perceived meaning as protective factors to consider when examining individuals who have been impacted by a specific technological disaster. Additionally, this study adds discrepant data to the assumption that posttraumatic stress differs by sex. Finally, this study adds to the movement in disaster mental health literature to broaden the focus to protective factors, recovery, and growth post-disaster. Implications for these data are discussed

Meaning, Resilience, And Traumatic Stress Following The Gulf Oil Spill: A Study Of Mississippi Coastal Residents Seeking Mental Health Services

In April of 2010, the Deepwater Horizon Oil Platform exploded, resulting in the release of millions of gallons of oil into the Gulf of Mexico over a period of three months. In addition to the ecological and economic impact of the disaster, the spill also had a significant impact on the psychological well-being of coastal residents. Following a disaster, not all affected people experience the same level of distress or long-term, negative psychological effects. Coping mechanisms such as resilience and perceived meaning in life are essential variables in understanding how people respond to a wide range of disasters. The present study examines the relationship between resilience, perceived meaning in life, and traumatic stress symptoms among coastal residents of Mississippi directly affected by the Gulf Oil Spill. The study was conducted as part of a larger project that assessed the impact of the Gulf Oil Spill on the mental health of individuals seeking therapeutic services ( N = 1119). It was predicted that meaning and resilience would be related to each other significantly and positively and that individuals with higher levels of resilience and/or perceived meaning in life would report significantly fewer symptoms of posttraumatic stress. After controlling for the impact of the spill, it was also predicted that both resilience and meaning would be significant predictors of posttraumatic stress symptoms and that adding meaning to the resilience model would make for a stronger model overall. Multiple hierarchical regression analysis was conducted to determine if resilience and perceived meaning are significant predictors of scores from a measure of posttraumatic stress. Meaning and resilience were found to be significantly and positive correlated. Higher levels of resilience and meaning separately were both predictive of lower levels of posttraumatic stress scores, and resilience and meaning together were predictive of posttraumatic stress after controlling for the impact of the spill. Based on the analyses, it is apparent that resilience and perceived meaning in life are similarly strong, significant predictors of fewer posttraumatic stress symptoms and these two constructs are highly correlated. Implications for these data are discussed

Local spectral theory for operators R and S satisfying RSR = R^2

We study some local spectral properties for bounded operators R, S, RS and SR in the case that R and S satisfy the operator equation RSR =R^2. Among other results, we prove that S, R, SR and RS share Dunford's property (C) when RSR = R^2and SRS =S^2peerReviewe

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

Further Properties of an Operator Commuting with an Injective Quasi-Nilpotent Operator

In (Aiena et al., Math. Proc. R. Irish Acad. 122A(2):101–116, 2022), it has been shown that a bounded linear operator T ∈ L(X), defined on an infinite-dimensional complex Banach space X, for which there exists an injective quasi-nilpotent operator that commutes with it, has a very special structure of the spectrum. In this paper, we show that we have much more: if a such quasi-nilpotent operator does exist, then some of the spectra of T originating from B-Fredholm theory coalesce. Further, the spectral mapping theorem holds for all the B-Weyl spectra. Finally, the generalized version of Weyl type theorems hold for T assuming that T is of polaroid type. Our results apply to the operators that belong to the commutant of Volterra operators