# Weak and weak* $I^K$-convergence in normed spaces

@article{Banerjee2018WeakAW, title={Weak and weak* \$I^K\$-convergence in normed spaces}, author={Amar Kumar Banerjee and Mahendranath Paul}, journal={arXiv: General Topology}, year={2018} }

The main object of this paper is to study the concept of weak $I^K$-convergence, a generalization of weak $I^*$-convergence of sequences in a normed space, introducing the idea of weak* $I^K$-convergence of sequences of functionals where $I,K$ are two ideals on $\mathbb{N}$, the set of all positive integers. Also we have studied the ideas of weak $I^K$ and weak* $I^K$-limit points to investigate the properties in the same space.

## One Citation

### ON A I K –SUMMABILITY

- Philosophy, Mathematics
- 2022

: In this paper, we introduce and investigate the concept of A I K -summability as an extension of A I ∗ -summability which was recently (2021) introduced by O.H.H. Edely, where A = ( a nk ) ∞ n,k =1…

## References

SHOWING 1-10 OF 26 REFERENCES

### WEAK IDEAL CONVERGENCE IN $l_p$ SPACES

- Mathematics
- 2012

In this paper, we see that how weak ideal convergence 'looks like' in lp spaces. We extend the recently introduced concept of weak ∗ statistical convergence to have a new concept of weak ∗ ideal…

### On weak ideal convergence in normed spaces

- Mathematics
- 2010

Abstract Recently, we have introduced the concepts of weak ideal convergence (briefly, weak I–convergence) and weak I–Cauchy sequence in a normed space, and investigated their basic properties [25].…

### A Note on I^K and I^K*-convergence in topological spaces

- Mathematics
- 2018

In this paper we have studied some important topological properties and characterization of I^K-convergence of functions which is a common generalization of I*-convergence of functions. We also…

### Strong-I^K-Convergence in Probabilistic Metric Spaces

- Mathematics
- 2018

In this paper we study the idea of strong-I^K-convergence of functions which is common generalization of strong-I*-convergence of functions in probabilistic metric spaces. We also study…

### A NOTE ON I-CONVERGENCE AND I ? -CONVERGENCE OF SEQUENCES AND NETS IN TOPOLOGICAL SPACES

- Mathematics
- 2015

In this paper, we use the idea of I-convergence and I ? -convergence of sequences and nets in a topological space to study some important topological properties. Further we derive characterization of…

### I-convergence classes of sequences and nets in topological spaces

- Mathematics
- 2016

In this paper we have used the idea of I-convergence of sequences and nets to study certain conditions of convergence in a topological space. It has been shown separately that a class of sequences…

### ON I AND I K -CAUCHY NETS AND COMPLETENESS

- Mathematics
- 2014

In this paper we study the concept of I K -Cauchy nets which is more general form of I -Cauchy nets ((4,5)). We also investigate its relation with the concept of I-Cauchy nets and study the…

### A characterization of Banach spaces with separable duals via weak statistical convergence

- Mathematics
- 2000

Abstract Let B be a Banach space. A B-valued sequence 〈 xk〉 is weakly statistically null provided lim n 1 n |{k ≤ n:|f(x k )| > e}| = 0 for all e > 0 and every continuous linear functional f on B. A…

### ON WEAK∗ STATISTICAL CONVERGENCE OF SEQUENCE OF FUNCTIONALS

- Philosophy, Mathematics
- 2011

The main object of this paper is to introduce the concept of weak∗ statistical convergence of sequence of functionals in a normed space. It is shown that in a reflexive space, weak∗ statistically…