Полу-Фредхолмови оператори на Хилбертовим C∗-модулима

In the first part of the thesis, we establish the semi-Fredholm theory on Hilbert C∗- modules as a continuation of the Fredholm theory on Hilbert C∗-modules which was introduced by Mishchenko and Fomenko. Starting from their definition of C∗-Fredholm operator, we give definition of semi-C∗-Fredholm operator and prove that these operators correspond to one-sided invertible elements in the Calkin algebra. Also, we give definition of semi-C∗-Weyl operators and semi-C∗-B-Fredholm operators and obtain in this connection several results generalizing the counterparts from the classical semi-Fredholm theory on Hilbert spaces. Finally, we consider closed range operators on Hilbert C∗-modules and give necessary and sufficient conditions for a composition of two closed range C∗-operators to have closed image. The second part of the thesis is devoted to the generalized spectral theory of operators on Hilbert C∗-modules. We introduce generalized spectra in C∗-algebras of C∗-operators and give description of such spectra of shift operators, unitary, self-adjoint and normal operators on the standard Hilbert C∗- module. Then we proceed further by studying generalized Fredholm spectra (in C∗-algebras) of operators on Hilbert C∗-modules induced by various subclasses of semi-C∗-Fredholm operators. In this setting we obtain generalizations of some of the results from the classical spectral semi-Fredholm theory such as the results by Zemanek regarding the relationship between the spectra of an operator and the spectra of its compressions. Also, we study 2×2 upper triangular operator matrices acting on the direct sum of two standard Hilbert C∗-modules and describe the relationship between semi-C∗-Fredholmness of these matrices and of their diagonal entries.У првом делу тезе успостављамо полу-Фредхолмову теориjу на Хилбертовим C∗- модулима као наставак Фредхолмове теориjе на Хилбертовим C∗-модулима коjу су увели Мишченко и Фоменко. Полазећи од њихове дефинициjе C∗-Фредхолмових оператора, даjе- мо дефинициjу полу-C∗-Фредхолмовог оператора и доказуjемо да ти оператори одговараjу jеднострано инвертибилним елементима у Калкиновоj алгебри. Такође, даjемо дефиници- jу полу-C∗-Ваjлових оператора и полу-C∗-Б-Фредхолмових оператора и добиjамо с тим у вези више резултата коjи генерализуjу пандане из класичне полу-Фредхолмове теориjе на Хилбертовим просторима. На краjу, разматрамо операторе са затвореном сликом на Хилбертовим C∗-модулима и даjемо потребне и довољне услове да композициjа два C∗- оператора са затвореном сликом има затворену слику. Други део тезе посвећен jе генера- лизованоj спектралноj теориjи оператора на Хилбертовим C∗-модулима. За C∗-операторе дефинишемо генерализоване спектре у C∗-алгебри и даjемо опис таквих спектара у кон- кретном случаjу оператора помака, унитарних, самоадjонгованих и нормалних оператора на стандардном Хилбертовом C∗-модулу. Затим настављамо даље проучаваjући генера- лизоване Фредхолмове спектре (у C∗-алгебрама) оператора на Хилбертовим C∗-модулима индукованим различитим подкласама полу-C∗-Фредхолмових оператора. У овом контек- сту добиjамо уопштење неких резултата из класичне спектралне полу-Фредхолмове теори- jе, као што су Земанекови резултати у вези релациjа између спектара оператора и спектара њихових компресиjа. Такође, проучавамо 2 × 2 горње триjангуларне операторске матрице коjе делуjу на директноj суми два стандардна Хилбертова C∗-модула и описуjемо однос између полу-C∗-Фредхолмности ових матрица и њихових диjагоналних елемената

Полу-Фредхолмови оператори на Хилбертовим C∗-модулима

In the first part of the thesis, we establish the semi-Fredholm theory on Hilbert C∗- modules as a continuation of the Fredholm theory on Hilbert C∗-modules which was introduced by Mishchenko and Fomenko. Starting from their definition of C∗-Fredholm operator, we give definition of semi-C∗-Fredholm operator and prove that these operators correspond to one-sided invertible elements in the Calkin algebra. Also, we give definition of semi-C∗-Weyl operators and semi-C∗-B-Fredholm operators and obtain in this connection several results generalizing the counterparts from the classical semi-Fredholm theory on Hilbert spaces. Finally, we consider closed range operators on Hilbert C∗-modules and give necessary and sufficient conditions for a composition of two closed range C∗-operators to have closed image. The second part of the thesis is devoted to the generalized spectral theory of operators on Hilbert C∗-modules. We introduce generalized spectra in C∗-algebras of C∗-operators and give description of such spectra of shift operators, unitary, self-adjoint and normal operators on the standard Hilbert C∗- module. Then we proceed further by studying generalized Fredholm spectra (in C∗-algebras) of operators on Hilbert C∗-modules induced by various subclasses of semi-C∗-Fredholm operators. In this setting we obtain generalizations of some of the results from the classical spectral semi-Fredholm theory such as the results by Zemanek regarding the relationship between the spectra of an operator and the spectra of its compressions. Also, we study 2×2 upper triangular operator matrices acting on the direct sum of two standard Hilbert C∗-modules and describe the relationship between semi-C∗-Fredholmness of these matrices and of their diagonal entries.У првом делу тезе успостављамо полу-Фредхолмову теориjу на Хилбертовим C∗- модулима као наставак Фредхолмове теориjе на Хилбертовим C∗-модулима коjу су увели Мишченко и Фоменко. Полазећи од њихове дефинициjе C∗-Фредхолмових оператора, даjе- мо дефинициjу полу-C∗-Фредхолмовог оператора и доказуjемо да ти оператори одговараjу jеднострано инвертибилним елементима у Калкиновоj алгебри. Такође, даjемо дефиници- jу полу-C∗-Ваjлових оператора и полу-C∗-Б-Фредхолмових оператора и добиjамо с тим у вези више резултата коjи генерализуjу пандане из класичне полу-Фредхолмове теориjе на Хилбертовим просторима. На краjу, разматрамо операторе са затвореном сликом на Хилбертовим C∗-модулима и даjемо потребне и довољне услове да композициjа два C∗- оператора са затвореном сликом има затворену слику. Други део тезе посвећен jе генера- лизованоj спектралноj теориjи оператора на Хилбертовим C∗-модулима. За C∗-операторе дефинишемо генерализоване спектре у C∗-алгебри и даjемо опис таквих спектара у кон- кретном случаjу оператора помака, унитарних, самоадjонгованих и нормалних оператора на стандардном Хилбертовом C∗-модулу. Затим настављамо даље проучаваjући генера- лизоване Фредхолмове спектре (у C∗-алгебрама) оператора на Хилбертовим C∗-модулима индукованим различитим подкласама полу-C∗-Фредхолмових оператора. У овом контек- сту добиjамо уопштење неких резултата из класичне спектралне полу-Фредхолмове теори- jе, као што су Земанекови резултати у вези релациjа између спектара оператора и спектара њихових компресиjа. Такође, проучавамо 2 × 2 горње триjангуларне операторске матрице коjе делуjу на директноj суми два стандардна Хилбертова C∗-модула и описуjемо однос између полу-C∗-Фредхолмности ових матрица и њихових диjагоналних елемената

Age and weather effects on between and within ring variations of number, width and coarseness of tracheids and radial growth of young Norway spruce

Annual growth, fibre and wood properties of Norway spruce are all under strong influence from genetics, age and weather. They change dynamically, particularly at young ages. Most genetic research and tree improvement programs are based on data from this most dynamic phase of the life of trees, affected by differences in weather among sites and years. In the work presented, influences of age and weather were investigated and modelled at the detail of annual rings and at the sub-tree ring level of earlywood, transitionwood and latewood. The data used were analysed from increment cores sampled at age 21 years from almost 6000 Norway spruce trees of known genetic origin, grown on two sites in southern Sweden. The traits under investigation were radial growth, cell widths, cell numbers, cell wall thickness and coarseness as a measure of biomass allocation at cell level. General additive mixed models (GAMMs) were fitted to model the influences of age, local temperature and precipitation. The best models were obtained for number of tracheids formed per year, ring width, average radial tracheid width in earlywood, and ring averages for tangential tracheid width and coarseness. Considering the many sources behind the huge variation, the explained part of the variability was high. For all traits, models were developed using both total tree age and cambial age (ring number) to express age. Comparisons indicate that the number of cell divisions and ring width are under stronger control of tree age, but the other traits under stronger control of cambial age. The models provide a basis to refine data prior to genetic evaluations by compensating for estimated differences between sites and years related to age and weather rather than genetics. Other expected applications are to predict performance of genotypes in relation to site or climate and simulation of climate change scenarios.Bio4Energ