zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the fine spectrum of the operator B(r,s,t) over the sequence spaces p and bv p ,(1<p<). (English) Zbl 1222.47050
The authors determine the exact location of the fine spectrum of a linear operator given by an infinite three-diagonal banded matrix in the sequence spaces p and bv p for p(1,). Their results generalize some earlier results of the authors and their collaborators on this subject.
MSC:
47B39Difference operators (operator theory)
40C05Matrix methods in summability
46B45Banach sequence spaces
References:
[1]Kreyszig, E.: Introductory functional analysis with applications, (1978)
[2]Goldberg, S.: Unbounded linear operators, (1985) · Zbl 0925.47001
[3]Gonzàlez, M.: The fine spectrum of the Cesàro operator in p(1p), Arch. math. 44, 355-358 (1985) · Zbl 0568.47021 · doi:10.1007/BF01235779
[4]J.P. Cartlidge, Weighted mean matrices as operators on p, Ph.D. Dissertation, Indiana University, 1978.
[5]Okutoyi, J. T.: On the spectrum of C1 as an operator on bv0, J. aust. Math. soc. Ser. A 48, 79-86 (1990) · Zbl 0691.40004
[6]Okutoyi, J. T.: On the spectrum of C1 as an operator on bv, Commun. fac. Sci. univ. Ank. sér. A1 41, 197-207 (1992) · Zbl 0831.47020
[7]Altay, B.; Başar, F.: On the fine spectrum of the difference operator on c0 and c, Inform. sci. 168, 217-224 (2004) · Zbl 1085.47041 · doi:10.1016/j.ins.2004.02.007
[8]Altay, B.; Başar, F.: On the fine spectrum of the generalized difference operator B(r,s) over the sequence spaces c0 and c, Int. J. Math. math. Sci. 2005, No. 18, 3005-3013 (2005) · Zbl 1098.39013 · doi:10.1155/IJMMS.2005.3005
[9]Kayaduman, K.; Furkan, H.: The fine specta of the difference operator Δ over the sequence spaces 1 and bv, Int. math. Forum 1, No. 24, 1153-1160 (2006) · Zbl 1119.47306
[10]Akhmedov, A. M.; Başar, F.: On the spectra of the difference operator Δ over the sequence space p, Demonstratio math. 39, No. 3, 585-595 (2006) · Zbl 1118.47303
[11]Akhmedov, A. M.; Başar, F.: On the fine spectra of the difference operator Δ over the sequence space bvp,1p, Acta math. Sin. (Engl. Ser.) 23, No. 10, 1757-1768 (2007) · Zbl 1134.47025 · doi:10.1007/s10114-005-0777-0
[12]Furkan, H.; Bilgiç, H.; Kayaduman, K.: On the fine spectrum of the generalized difference operator B(r,s) over the sequence spaces 1 and bv, Hokkaido math. J. 35, 897-908 (2006) · Zbl 1119.47005
[13]Furkan, H.; Bilgiç, H.; Altay, B.: On the fine spectrum of the operator B(r,s,t) over c0 and c, Comput. math. Appl. 53, No. 6, 989-998 (2007) · Zbl 1124.47024 · doi:10.1016/j.camwa.2006.07.006
[14]Bilgiç, H.; Furkan, H.: On the fine spectrum of the operator B(r,s,t) over the sequence spaces 1 and bv, Math. comput. Modelling 45, No. 7–8, 883-891 (2007) · Zbl 1152.47024 · doi:10.1016/j.mcm.2006.08.008
[15]Bilgiç, H.; Furkan, H.: On the fine spectrum of the generalized difference operator B(r,s) over the sequence spaces p and bvp(1p), Nonlinear anal. 68, No. 3, 499-506 (2008) · Zbl 1139.47005 · doi:10.1016/j.na.2006.11.015
[16]Altay, B.; Başar, F.: On the space of sequences of p-bounded variation and related matrix mappings, Ukrainian math. J. 55, No. 1, 136-147 (2003) · Zbl 1040.46022 · doi:10.1023/A:1025080820961
[17]Imaninezhad, M.; Miri, M. R.: The dual space of the sequence space bvp,(1p), Acta math. Univ. comenian. 79, No. 1, 143-149 (2010) · Zbl 1212.46023
[18]Choudhary, B.; Nanda, S.: Functional analysis with applications, (1989) · Zbl 0698.46001