Generalized atomic subspaces for operators in Hilbert spaces

Prasenjit Ghosh; Tapas Kumar Samanta

Mathematica Bohemica (2022)

  • Volume: 147, Issue: 3, page 325-345
  • ISSN: 0862-7959

Abstract

top
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.

How to cite

top

Ghosh, Prasenjit, and Samanta, Tapas Kumar. "Generalized atomic subspaces for operators in Hilbert spaces." Mathematica Bohemica 147.3 (2022): 325-345. <http://eudml.org/doc/298481>.

@article{Ghosh2022,
abstract = {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.},
author = {Ghosh, Prasenjit, Samanta, Tapas Kumar},
journal = {Mathematica Bohemica},
keywords = {frame; atomic subspace; $g$-fusion frame; $K$-$g$-fusion frame},
language = {eng},
number = {3},
pages = {325-345},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized atomic subspaces for operators in Hilbert spaces},
url = {http://eudml.org/doc/298481},
volume = {147},
year = {2022},
}

TY - JOUR
AU - Ghosh, Prasenjit
AU - Samanta, Tapas Kumar
TI - Generalized atomic subspaces for operators in Hilbert spaces
JO - Mathematica Bohemica
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 147
IS - 3
SP - 325
EP - 345
AB - 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.
LA - eng
KW - frame; atomic subspace; $g$-fusion frame; $K$-$g$-fusion frame
UR - http://eudml.org/doc/298481
ER -

References

top
  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. (2020) MR4136053
  2. Bhandari, A., Mukherjee, S., 10.1007/s13226-020-0448-y, Indian J. Pure Appl. Math. 51 (2020), 1039-1052. (2020) Zbl1456.42037MR4159339DOI10.1007/s13226-020-0448-y
  3. Casazza, P. G., Kutyniok, G., 10.1090/conm/345, Wavelets, Frames and Operator Theory Contemporary Mathematics 345. American Mathematical Society, Providence (2004), 87-114. (2004) Zbl1058.42019MR2066823DOI10.1090/conm/345
  4. Christensen, O., 10.1007/978-3-319-25613-9, Applied and Numerical Harmonic Analysis. Birkhäuser, Basel (2016). (2016) Zbl1348.42033MR3495345DOI10.1007/978-3-319-25613-9
  5. Daubechies, I., Grossmann, A., Meyer, Y., 10.1063/1.527388, J. Math. Phys. 27 (1986), 1271-1283. (1986) Zbl0608.46014MR0836025DOI10.1063/1.527388
  6. Douglas, R. G., 10.1090/S0002-9939-1966-0203464-1, Proc. Am. Math. Soc. 17 (1966), 413-415. (1966) Zbl0146.12503MR0203464DOI10.1090/S0002-9939-1966-0203464-1
  7. Duffin, R. J., Schaeffer, A. C., 10.1090/S0002-9947-1952-0047179-6, Trans. Am. Math. Soc. 72 (1952), 341-366. (1952) Zbl0049.32401MR0047179DOI10.1090/S0002-9947-1952-0047179-6
  8. Găvruţa, L., 10.1016/j.acha.2011.07.006, Appl. Comput. Harmon. Anal. 32 (2012), 139-144. (2012) Zbl1230.42038MR2854166DOI10.1016/j.acha.2011.07.006
  9. Găvruţa, L., Atomic decompositions for operators in reproducing kernel Hilbert spaces, Math. Rep., Buchar. 17 (2015), 303-314. (2015) Zbl1374.42057MR3417770
  10. Găvruţa, P., 10.1016/j.jmaa.2006.11.052, J. Math. Anal. Appl. 333 (2007), 871-879. (2007) Zbl1127.46016MR2331700DOI10.1016/j.jmaa.2006.11.052
  11. Ghosh, P., Samanta, T. K., 10.31392/MFAT-npu26_3.2020.04, Methods Funct. Anal. Topology 26 (2020), 227-240. (2020) MR4165154DOI10.31392/MFAT-npu26_3.2020.04
  12. Hua, D., Huang, Y., 10.4134/JKMS.j150499, J. Korean Math. Soc. 53 (2016), 1331-1345. (2016) Zbl1358.42026MR3570976DOI10.4134/JKMS.j150499
  13. Pawan, K. J., Om, P. A., Functional Analysis, New Age International Publisher, New Delhi (1995). (1995) 
  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. (2018) 
  15. Sun, W., 10.1016/j.jmaa.2005.09.039, J. Math. Anal. Appl. 322 (2006), 437-452. (2006) Zbl1129.42017MR2239250DOI10.1016/j.jmaa.2005.09.039

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.