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Table 3 The characterization of the class ( λ ˜ :μ) with λ{ ,c, c 0 , p , 1 } and μ{ ,c, c 0 , 1 }

From: Domain of the double sequential band matrix in the classical sequence spaces

To

From

˜

c ˜

c ˜ 0

˜ p

˜ 1

1.

2.

3.

4.

5.

c

6.

7.

8.

9.

10.

c 0

11.

12.

13.

14.

15.

1

16.

17.

18.

19.

20.

  1. Here 1. (4.5), (4.6) and (4.9) with q = 1. 2. (4.5), (4.7) and (4.4), (4.9) with q = 1. 3. (4.5) and (4.4), (4.9) with q = 1. 4. (4.4), (4.5) and (4.9). 5. (4.5), (4.8) and (4.13). 6. (4.5), (4.6), (4.10) and (4.11). 7. (4.5), (4.7), (4.10), (4.12) and (4.4), (4.9) with q = 1. 8. (4.5), (4.10) and (4.4), (4.9) with q = 1. 9. (4.4), (4.5), (4.9) and (4.10). 10. (4.5), (4.8), (4.10) and (4.13). 11. (4.5), (4.6) and (4.15). 12. (4.5), (4.7), (4.10) with β k =0 and (4.12) with β = 0, and (4.4), (4.9) with q = 1. 13. (4.5), (4.10) with β k =0 and (4.4), (4.9) with q = 1. 14. (4.4), (4.5), (4.9) and (4.10) with β k =0. 15. (4.5), (4.8), (4.10) with β k =0 and (4.13). 16. (4.5), (4.6) and (4.16). 17. (4.4) with q = 1, (4.5), (4.7) and (4.16). 18. (4.4) with q = 1, (4.5) and (4.16). 19. (4.4), (4.5) and (4.17). 20. (4.5), (4.8) and (4.14).