| dc.date.accessioned |
2022-03-30T05:32:49Z |
|
| dc.date.available |
2022-03-30T05:32:49Z |
|
| dc.date.issued |
2022-03-30 |
|
| dc.identifier.uri |
http://hdl.handle.net/123456789/39990 |
|
| dc.title |
P-Fredholmness of Band-dominated Operators, and its Equivalence to Invertibility of Limit Operators and the Uniform Boundedness of Their Inverses |
en |
| ethesis.faculty |
Matemaattis-luonnontieteellinen tiedekunta |
fi |
| ethesis.faculty |
Faculty of Science |
en |
| ethesis.faculty |
Matematisk-naturvetenskapliga fakulteten |
sv |
| ethesis.faculty.URI |
http://data.hulib.helsinki.fi/id/8d59209f-6614-4edd-9744-1ebdaf1d13ca |
|
| ethesis.university.URI |
http://data.hulib.helsinki.fi/id/50ae46d8-7ba9-4821-877c-c994c78b0d97 |
|
| ethesis.university |
Helsingin yliopisto |
fi |
| ethesis.university |
University of Helsinki |
en |
| ethesis.university |
Helsingfors universitet |
sv |
| dct.creator |
Moilanen, Eero |
|
| dct.issued |
2022 |
xx |
| dct.abstract |
In the thesis ”P-Fredholmness of Band-dominated Operators, and its Equivalence to Invertibility of Limit Operators
and the Uniform Boundedness of Their Inverses”, we present the generalization of the classical Fredholm-Riesz
theory with respect to a sequence of approximating projections on direct sums of spaces. The thesis is a progessive
introduction to understanding and proving the core result in the generalized Fredholm-Riesz theory, which is stated
in the title. The stated equivalence has been further improved and it can be generalized further by omitting either
the initial condition of richness of the operator or the uniform boundedness criterion. Our focal point is on the
elementary form of this result.
We lay the groundwork for the classical Fredholm-Riesz theory by introducing compact operators and defining
Fredholmness as invertibility on modulo compact operators. Thereafter we introduce the concept of approximating
projections in infinite direct sums of Banach spaces, that is we operate continuous operators with a sequence of
projections which approach the identity operator in the limit and examine whether we have convergence in the
norm sense. This method yields us a way to define P-compactness, P-strong converngence and finally PFredholmness.
We introduce the notion of limit operators operators by first shifting, then operating and then shifting back an
operator with respect to an element in a sequence and afterwards investigating what happens in the P-strong limit
of this sequence. Furthermore we define band-dominated operators as uniform limits of linear combinations of
simple multiplication and shift operators. In this subspace of operators we prove that indeed for rich operators the
core result holds true. |
en |
| ethesis.isPublicationLicenseAccepted |
true |
|
| ethesis.language.URI |
http://data.hulib.helsinki.fi/id/languages/eng |
|
| ethesis.language |
englanti |
fi |
| ethesis.language |
English |
en |
| ethesis.language |
engelska |
sv |
| ethesis.thesistype |
pro gradu -tutkielmat |
fi |
| ethesis.thesistype |
master's thesis |
en |
| ethesis.thesistype |
pro gradu-avhandlingar |
sv |
| ethesis.thesistype.URI |
http://data.hulib.helsinki.fi/id/thesistypes/mastersthesis |
|
| dct.identifier.ethesis |
E-thesisID:3cb3c9d4-78ae-4a11-b0a1-962e0d2b2201 |
|
| dct.identifier.urn |
URN:NBN:fi:hulib-202203301558 |
|
| ethesis.facultystudyline |
Matematiikka |
fi |
| ethesis.facultystudyline |
Mathematics |
en |
| ethesis.facultystudyline |
Matematik |
sv |
| ethesis.facultystudyline.URI |
http://data.hulib.helsinki.fi/id/SH50_050 |
|
| ethesis.mastersdegreeprogram |
Matematiikan ja tilastotieteen maisteriohjelma |
fi |
| ethesis.mastersdegreeprogram |
Master 's Programme in Mathematics and Statistics |
en |
| ethesis.mastersdegreeprogram |
Magisterprogrammet i matematik och statistik |
sv |
| ethesis.mastersdegreeprogram.URI |
http://data.hulib.helsinki.fi/id/MH50_001 |
|
