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 over the sequence space c. (English) Zbl 1222.40002
Summary: We examine the fine spectrum of the generalized difference operator Δ a,b over the sequence space c. The boundedness of the operator Δ a,b is proved. Also, the norm of this operator is found. The class of the operator Δ a,b includes some other special cases such as the generalized difference operator B(r,s) introduced by B. Altay and F. Başar [Int. J. Math. Math. Sci. 2005, No. 18, 3005–3013 (2005; Zbl 1098.39013)]. Our results not only generalize the corresponding results in the existing literature, but also give results for some more operators.
MSC:
40C05Matrix methods in summability
47B37Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
40H05Functional analytic methods in summability
47A10Spectrum and resolvent of linear operators
References:
[1]Kreyszig, E.: Introductory functional analysis with applications, (1978)
[2]Goldberg, S.: Unbounded linear operators, (1985) · Zbl 0925.47001
[3]Akhmedov, A. M.: On the spectrum of the generalized difference operator Δα over the sequence space lp,(1p), Baku univ. News J., phys. Math. sci. Ser. 3, 34-39 (2009)
[4]Altay, B.; Başar, F.: On the fine spectrum of the difference operator Δ on c0 and c, Inform. sci. 168, 217-224 (2004) · Zbl 1085.47041 · doi:10.1016/j.ins.2004.02.007
[5]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. 18, 3005-3013 (2005) · Zbl 1098.39013 · doi:10.1155/IJMMS.2005.3005
[6]Altay, B.; Karakuş, M.: On the spectrum and the fine spectrum of the zweier matrix as an operator on some sequence spaces, Thai J. Math. 3, No. 2, 153-162 (2005) · Zbl 1183.47027 · doi:http://math.science.cmu.ac.th/thaijournal/completed32/Bilal3.pdf
[7]Srivastava, P. D.; Kumar, S.: On the fine spectrum of the generalized difference operator Δv over the sequence space c0, Commun. math. Anal. 6, No. 1, 8-21 (2009) · Zbl 1173.47022
[8]Wilansky, A.: Summability through functional analysis, North-holland mathematics studies 85 (1984) · Zbl 0531.40008
[9]Akhmedov, A. M.; Başar, F.: On the fine spectra of the difference operator Δ over the sequence space lp,(1p), Demonstratio math. 39, No. 3, 585-595 (2006) · Zbl 1118.47303
[10]Akhmedov, A. M.; Başar, F.: 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
[11]Başar, F.; Altay, B.: 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
[12]De Malafosse, B.: Properties of some sets of sequences and application to the spaces of bounded difference sequences of order μ, Hokkaido math. J. 31, 283-299 (2002) · Zbl 1016.40002
[13]Bilgiç, H.; Furkan, H.: On the fine spectrum of the generalized difference operator B(r,s) over the sequence spaces lp and bvp,(1p), Nonlinear anal. 68, 499-506 (2008) · Zbl 1139.47005 · doi:10.1016/j.na.2006.11.015
[14]Srivastava, P. D.; Kumar, S.: Fine spectrum of the generalized difference operator Δv on sequence space l1, Thai J. Math. 8, No. 2, 221-233 (2010)
[15]Panigrahi, B. L.; Srivastava, P. D.: Spectrum and fine spectrum of generalized second order difference operator Δuv2 on sequence space c0, Thai J. Math. 9, No. 1, 57-74 (2011)
[16]Furkan, H.; Bilgiç, H.; Başar, F.: On the fine spectrum of the operator B(r,s,t) over the sequence spaces lp and bvp,(1p), Comput. math. Appl. 60, No. 7, 2141-2152 (2010) · Zbl 1222.47050 · doi:10.1016/j.camwa.2010.07.059
[17]J.P. Cartlidge, Weighted mean matrices as operators on lp, Ph.D. Dissertation, Indiana Univ., Indiana, 1978.