Invariant subspaces of operators quasi-similar to L-weakly and M-weakly compact operators

Let T be an L-weakly compact operator defined on a Banach lattice E without order continuous norm. We prove that the bounded operator S defined on a Banach space X has a nontrivial closed invariant subspace if there exists an operator in the commutant of S that is quasi-similar to T. Additively, some similar and relevant results are extended to a larger classes of operators called super right-commutant. We also show that quasi-similarity need not preserve L-weakly or M-weakly compactness.Scientific and Technological Research Council of TurkeyTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK); Research Foundation of Namik Kemal UniversityNamik Kemal University [NKUBAP.00.10.AR.15.04]The author is grateful to Professor AW Wickstead for some useful comments and suggestions, which improved the paper. Author was supported by the Scientific and Technological Research Council of Turkey in the context of the 2219-Postdoctoral Fellowship Program and by the Research Foundation of Namik Kemal University (Project No: NKUBAP.00.10.AR.15.04)

On the invariant supspace problem

In this study, we present invariant subspaces (subideals) for a class of operators (positive operators) related to M-weakly and L-weakly compact operators. Principally, these invariant subspaces can be conceivable for all operators that commutes with any M-weakly or L-weakly compact operator. © 2013 Academic Publications, Ltd

LACUNARY STATISTICAL CONVERGENCE OF ORDER α IN PARTIAL METRIC SPACES

The present study introduces the notions of statistical convergence of order $\alpha$ and strongly $q-$ summability of order $\alpha$ in partial metric spaces. We examinethe inclusion relations linked to these these concepts

M-Zayıf Kompakt Operatörler İçin Merkezin İncelenmesi

E sıralı vektör uzayı üzerinde tanımlı T operatörü özdeşlik dönüşümünün bir skalar katı olarak yazılabiliyorsa, yani her bir x?E+ için -?x ? Tx ? ?x olacak biçimde bir ? > 0 skalar sayısı varsa, T 'ye merkez operatörü denir. Tüm merkez operatörleri sınıfı E 'nin merkezi denir ve Z?E? ile gösterilir. Özellikle vektör örgülerinin merkezleri üzerine yapılan çok sayıda çalışma arasında, regüler operatörlerin çeşitli sınıflarının merkezlerinin tanımlama çabaları vardır. E ve F Banach örgüsü ve Z?E? Z?F? injektif tensör çarpım normu ile verildiğinde Z?E? Z?F? den ? ? ?? r Z L E,F içine bir izometrik gömme dönüşümünün var olduğu verilmiştir. Üstelik bu ve benzer gömme dönüşümlerine ilişkin bazı yoğunluk sonuçları da verilmiştir. Ayrıca, kompakt ve zayıf kompakt operatörler için ilgili sonuçlarda elde edilmiştir. Bu çalışmada, Banach örgüleri arasında tanımlı regüler, kompakt ve zayıf kompakt operatörlerin merkezleri için verilen sonuçları L-zayıf ve M-zayıf kompakt operatörler bağlamında genişlettik. Ayrıca, bir Banach örgüsünün merkezindeki kompakt operatörler ile L-zayıf ve M-zayıf kompakt operatörlerin çakıştıklarını ispatladık.An operator T on an ordered vector space E, with positive cone + E , is called central if it is bounded by a multiple of the identity operator, i.e., there exists some scalar ? > 0 such that -?x ? Tx ? ?x holds for all ? + x E . The collection of all central operators on E is called the centre of E and denoted by Z?E? . Amongst many works on the centre, especially in the context of vector lattices, there have been attempts to identify the centre of various spaces of regular operators. Some isometric results were given showing that if E and F are Banach lattices then there is an embedding of the algebraic tensor product Z?E? Z?F? into ? ? ?? r Z L E,F which is an isometry when Z?E? Z?F? is given the injective tensor product norm. Furthermore, it is also given some density results regarding this, and similar, embeddings. Also, some related results are obtained for spaces of compact and weakly compact operators. In this study we extend and modified known results concerning the centre of spaces of regular (resp. weakly compact or compact) operators between two Banach lattices to the setting of L-weakly compact and M-weakly compact operators. We also show that the L-weakly compact, M-weakly compact and compact operators lying in the centre of a Banach lattice coincide

On the Order Structure of L- and M-weakly Compact Operators

Banach örgüleri üzerinde tanımlı zayıf kompakt operatörlerin alt sınıfları olan L-zayıf ve M-zayıf kompaktoperatörlerin genelde vektör örgüsü olmadıkları bilinmesine rağmen sıra yapılarına dair çalışmalar literatürdegörünmemektedir. Birçok operatör sınıfının aksine baskınlık özelliğine sahip olmalarının bir sonucu olarak, yakınzamanda daha dar bir sınıf olan pozitif L-zayıf ve pozitif M-zayıf kompakt operatörlerin ürettiği sınıfların, sırayapılarına ilişkin sahip oldukları önemli özellikler verilmiştir [3]. Sunulan çalışmada da bu sonuçların bir devamıniteliğinde olan, söz konusu operatör sınıflarının regüler operatörler sınıfı içinde band ve KB-uzay olmakoşullarına dair bazı sonuçlar verilmiştir. Ayrıca L-zayıf veya M-zayıf kompakt operatörler, regüler olanları vepozitif olanları ile üretilmiş sınıfların çakıştıkları durumlar da irdelenmiştiAlthough it is known that L-weakly and M-weakly compact operators, which constitute the subclasses of weakly compact operators defined on Banach lattices, are not generally vector lattice, there are no sufficient studies in literature about their order structures. As a result of their domination property, which other operator classes do not possess, important features of order structures of the linear span of L-weakly and M-weakly compact operators have been recently revealed in [3]. As a continuation of such an attemt, our study presents certain results about the conditions of our operators to be the band and KB-space in the regular operators. In addition, the present study examines the equality properties of the classes of L-weakly or M-weakly compact operators, the regular ones, and the operators generated by positive ones

On Statistical Convergence Of Order α{\alpha} In Partial Metric Spaces

The present study introduces the notions of statistical convergence of order $\alpha$ and strong $p-$ Ces\`{a}ro summability of order $\alpha$ in partial metric spaces. Also, we examine the inclusion relations between these concepts. In addition, we introduce the notion of $\lambda -$% statistical convergence of order $\alpha$ in partial metric spaces while providing relations linked to these sequence spaces.Comment: 12 pag

İşbirliği süreci ölçeği (İSÖ) geliştirilmesi

One of the most important components of social constructivist learning environment is that learners are in co-operation. Effectiveness of cooperative learning process also depends on implementing the requirements of cooperative learning by the learners. The key components of cooperative learning are those positive dependence, personal responsibility, face-to-face supportive interaction, group process, interpersonal social skills. The purpose of this study has taken place to determine the psychometric properties of the measurement tool that was developed to examine effectiveness of cooperative learning process. The study was carried out on 177 students at the Gaziantep University, Faculty of Education. Learning environment was instructed under the social constructivist approach and the students have done their assigned tasks in cooperation with. 48-item test was applied to students. Factor analysis was implemented to the obtained data. Results of the study indicated that measurement tool should be used to measure process of cooperative learning.Sosyal yapılandırmacı öğrenme ortamının en önemli bileşenlerinden biri öğrenenlerin işbirliği içerisinde olmalarıdır. İşbirlikli öğrenme sürecinin etkililiği bu süreçte öğrenenlerin işbirlikli öğrenmenin gerekliliklerini yerine getirmelerini de bağlıdır. İşbirlikli öğrenmenin anahtar bileşenleri, olumlu bağlılık, bireysel sorumluluk, yüz yüze destekleyici etkileşim, grup süreci, kişiler arası sosyal becerilerdir.  Bu çalışmanın amacı, işbirlikli öğrenmedeki, bu sürecin gerçekleşip gerçekleşmediğini belirlemeye yönelik geliştirilen ölçme aracının psikometrik özelliklerini incelemektir. Çalışma Gaziantep Üniversitesi Gaziantep Eğitim Fakültesi’nde “Öğretim ilke ve yöntemleri” dersine devam eden 177 öğretmen adayı üzerinde gerçekleştirilmiştir. Araştırma kapsamında sosyal yapılandırmacı yaklaşıma dayalı öğrenme ortamları oluşturulmuştur ve öğretmen adayları kendilerine verilen görevleri işbirliği içerisinde gerçekleştirmişlerdir. 48 maddelik deneme formu öğrenenlere uygulanmıştır. Elde edilen veriler üzerinde faktör analizi uygulanmıştır. Bulgular geliştirilen ölçme aracının işbirlikli öğrenme sürecinin olması gerektiği gibi gerçekleşip gerçekleşmediğini belirlemeye yönelik olarak kullanılabileceğini göstermektedir. Ayrıca ölçme aracı tek ve beş boyutlu olarak kullanılabilmektedir

Absorption and Fluorescence Spectroscopy of 1,2 : 3,4-Dibenzanthracene

Polycyclic aromatic hydrocarbon compound, 1,2 : 3,4-dibenzanthracene, is spectroscopically analyzed in ethanol. Ultraviolet absorption spectra were taken and fluorescence measurements were performed. From absorption and emission spectra, Stokes' lines were clearly discernible and these shifts were recorded. Being a carcinogenic compound, the detection of 1,2 : 3,4-dibenzanthracene presence in the environment as a pollutant with adverse genotoxic effects is vital

Optical Energy Transfer Mechanisms: From Naphthalene to Biacetyl in Liquids and from Pyrazine to Biacetyl

Optical energy transfer from naphthalene to biacetyl in liquids at room temperature is studied. Electronically excited naphthalene with 200–260 nm ultraviolet (UV) light emits photons in its emission band and the emitted photons are absorbed by biacetyl, which, in turn, excites biacetyl phosphorescence. The resulting phosphorescence is very stable with emission peak at 545 nm for different excitation wavelengths from 200 to 260 nm. Similar optical energy transfer is also observed from pyrazine to biacetyl. The sensitization of biacetyl by several aromatic donors has been investigated in detail. An aromatic donor, pyrazine, is raised to its first excited singlet state by absorption of ultraviolet radiation. Excitation wavelengths were selected in the first - band of pyrazine. Intersystem crossing in pyrazine is sufficiently fast to give a triplet yield of almost unity as determined by the biacetyl method. The optical excess energy in the biacetyl will be released as light, which is sensitized fluorescence. Biacetyl is the simplest molecule among a wide range of -dicarbonyl compounds, which is important for photophysics and photochemistry applications

Unsustainable harvest of water frogs in southern Turkey for the European market

Frogs have been harvested from the wild for the last 40 years in Turkey. We analysed the population dynamics of Anatolian water frogs (Pelophylax spp.) in the Seyhan and Ceyhan Deltas during 2013–2015. We marked a total of 13,811 individuals during 3 years, estimated population sizes, simulated the dynamics of a harvested population over 50 years, and collated frog harvest and export statistics from the region and for Turkey as a whole. Our capture estimates indicated a population reduction of c. 20% per year, and our population modelling showed that, if overharvesting continues at current rates, the harvested populations will decline rapidly. Simulations with a model of harvested population dynamics resulted in a risk of extinction of > 90% within 50 years, with extinction likely in c. 2032. Our interviews with harvesters revealed their economic dependence on the frog harvest. However, our results also showed that reducing harvest rates would not only ensure the viability of these frog populations but would also provide a source of income that is sustainable in the long term. Our study provides insights into the position of Turkey in the ‘extinction domino’ line, in which harvest pressure shifts among countries as frog populations are depleted and harvest bans are effected. We recommend that harvesting of wild frogs should be banned during the mating season, hunting and exporting of frogs < 30 g should be banned, and harvesters should be trained on species knowledge and awareness of regulations