| Title:
|
Generalized atomic subspaces for operators in Hilbert spaces (English) |
| Author:
|
Ghosh, Prasenjit |
| Author:
|
Samanta, Tapas Kumar |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
147 |
| Issue:
|
3 |
| Year:
|
2022 |
| Pages:
|
325-345 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce the notion of a $g$-atomic subspace for a bounded linear operator and construct several useful resolutions of the identity operator on a Hilbert space using the theory of $g$-fusion frames. Also, we shall describe the concept of frame operator for a pair of $g$-fusion Bessel sequences and some of their properties. (English) |
| Keyword:
|
frame |
| Keyword:
|
atomic subspace |
| Keyword:
|
$g$-fusion frame |
| Keyword:
|
$K$-$g$-fusion frame |
| MSC:
|
42C15 |
| MSC:
|
46C07 |
| idZBL:
|
Zbl 07584128 |
| idMR:
|
MR4482309 |
| DOI:
|
10.21136/MB.2021.0130-20 |
| . |
| Date available:
|
2022-09-05T09:37:30Z |
| Last updated:
|
2022-12-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151011 |
| . |
| Reference:
|
[1] Ahmadi, R., Rahimlou, G., Sadri, V., Farfar, R. Zarghami: Constructions of $K$-g-fusion frames and their duals in Hilbert spaces.Bull. Transilv. Univ. Braşov, Ser. III, Math. Inform. Phys. 13 (2020), 17-32. MR 4136053 |
| Reference:
|
[2] Bhandari, A., Mukherjee, S.: Atomic subspaces for operators.Indian J. Pure Appl. Math. 51 (2020), 1039-1052. Zbl 1456.42037, MR 4159339, 10.1007/s13226-020-0448-y |
| Reference:
|
[3] Casazza, P. G., Kutyniok, G.: Frames of subspaces.Wavelets, Frames and Operator Theory Contemporary Mathematics 345. American Mathematical Society, Providence (2004), 87-114. Zbl 1058.42019, MR 2066823, 10.1090/conm/345 |
| Reference:
|
[4] Christensen, O.: An Introduction to Frames and Riesz Bases.Applied and Numerical Harmonic Analysis. Birkhäuser, Basel (2016). Zbl 1348.42033, MR 3495345, 10.1007/978-3-319-25613-9 |
| Reference:
|
[5] Daubechies, I., Grossmann, A., Meyer, Y.: Painless nonorthogonal expansions.J. Math. Phys. 27 (1986), 1271-1283. Zbl 0608.46014, MR 0836025, 10.1063/1.527388 |
| Reference:
|
[6] Douglas, R. G.: On majorization, factorization, and range inclusion of operators on Hilbert space.Proc. Am. Math. Soc. 17 (1966), 413-415. Zbl 0146.12503, MR 0203464, 10.1090/S0002-9939-1966-0203464-1 |
| Reference:
|
[7] Duffin, R. J., Schaeffer, A. C.: A class of nonharmonic Fourier series.Trans. Am. Math. Soc. 72 (1952), 341-366. Zbl 0049.32401, MR 0047179, 10.1090/S0002-9947-1952-0047179-6 |
| Reference:
|
[8] Găvruţa, L.: Frames for operators.Appl. Comput. Harmon. Anal. 32 (2012), 139-144. Zbl 1230.42038, MR 2854166, 10.1016/j.acha.2011.07.006 |
| Reference:
|
[9] Găvruţa, L.: Atomic decompositions for operators in reproducing kernel Hilbert spaces.Math. Rep., Buchar. 17 (2015), 303-314. Zbl 1374.42057, MR 3417770 |
| Reference:
|
[10] Găvruţa, P.: On the duality of fusion frames.J. Math. Anal. Appl. 333 (2007), 871-879. Zbl 1127.46016, MR 2331700, 10.1016/j.jmaa.2006.11.052 |
| Reference:
|
[11] Ghosh, P., Samanta, T. K.: Stability of dual $g$-fusion frames in Hilbert spaces.Methods Funct. Anal. Topology 26 (2020), 227-240. MR 4165154, 10.31392/MFAT-npu26_3.2020.04 |
| Reference:
|
[12] Hua, D., Huang, Y.: $K$-g-frames and stability of $K$-g-frames in Hilbert spaces.J. Korean Math. Soc. 53 (2016), 1331-1345. Zbl 1358.42026, MR 3570976, 10.4134/JKMS.j150499 |
| Reference:
|
[13] Pawan, K. J., Om, P. A.: Functional Analysis.New Age International Publisher, New Delhi (1995). |
| Reference:
|
[14] Sadri, V., Rahimlou, G., Ahmadi, R., Zarghami, R.: Generalized fusion frames in Hilbert spaces.Available at https://arxiv.org/abs/1806.03598v1 (2018), 16 pages. |
| Reference:
|
[15] Sun, W.: $g$-frames and $g$-Riesz bases.J. Math. Anal. Appl. 322 (2006), 437-452. Zbl 1129.42017, MR 2239250, 10.1016/j.jmaa.2005.09.039 |
| . |
