Fredholm theory for demicompact linear relations
Submitted: 2021-12-25
|Accepted: 2022-05-10
|Published: 2022-10-03
Copyright (c) 2022 Applied General Topology
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Downloads
Keywords:
demicompact linear relations, Fredholm theory, block matrix
Supporting agencies:
Abstract:
We first attempt to determine conditions on a linear relation T such that μT becomes a demicompact linear relation for each μ ∈ [0,1)(see Theorems 2.4 and 2.5). Second, we display some results on Fredholm and upper semi-Fredholm linear relations involving a demicompact one(see Theorems 3.1 and 3.2). Finally, we provide some results in which a block matrix of linear relations becomes a demicompact block matrix of linear relations (see Theorems 4.2 and 4.3).
References:
F. Abdmouleh, T. Álvarez, A. Ammar and A. Jeribi, Spectral mapping theorem for Rakocević and Schmoeger essential spectra of a multivalued linear operator, Mediterr. J. Math. 12, no. 3 (2015), 1019-1031. https://doi.org/10.1007/s00009-014-0437-7
A. Ammar, A characterization of some subsets of essential spectra of a multivalued linear operator, Complex Anal. Oper. Theory 11, no. 1 (2017), 175-196. https://doi.org/10.1007/s11785-016-0591-y
A. Ammar, Some results on semi-Fredholm perturbations of multivalued linear operators, Linear Multilinear Algebra 66, no. 7 (2018), 1311-1332. https://doi.org/10.1080/03081087.2017.1351517
A. Ammar, H. Daoud and A. Jeribi, Demicompact and K-D-setcontractive multivalued linear operators, Mediterr. J. Math. 15, no. 2 (2018): 41. https://doi.org/10.1007/s00009-018-1078-z
A. Ammar, S. Fakhfakh and A. Jeribi, Stability of the essential spectrum of the diagonally and off-diagonally dominant block matrix linear relations, J. Pseudo-Differ. Oper. Appl. 7, no. 4 (2016), 493-509. https://doi.org/10.1007/s11868-016-0154-z
W. Chaker, A. Jeribi and B. Krichen, Demicompact linear operators, essential spectrum and some perturbation results, Math. Nachr. 288, no. 13 (2015), 1476-1486. https://doi.org/10.1002/mana.201200007
R. W. Cross, Multivalued Linear Operators, Marcel Dekker, (1998).
A. Jeribi, Spectral Theory and Applications of Linear Operator and Block Operator Matrices, Springer-Verlag, New York, 2015. https://doi.org/10.1007/978-3-319-17566-9
K. Kuratowski, Sur les espaces complets, Fund. Math. 15 (1930), 301-309. https://doi.org/10.4064/fm-15-1-301-309
W. V. Petryshyn, Remarks on condensing and k-set-contractive mappings, J. Math. Appl. 39 (1972),3 717-741. https://doi.org/10.1016/0022-247X(72)90194-1
