1. Study of Equi – Continuous Spaces in Linear Topolgical Spaces

    Binod Prasad1, Md Shahabuddin2, Pramod Kumar Pandey3, Suresh Kumar Shukla4 & Umesh Kumar Srivastava5

    1. T.R.M. Campus, Birganj, Nepal, Tribhuvan University, Nepal. Mob. (Whatsapp) : 977,985 – 5035185, Email Id : bp97251@gmail.com
    2. P.R.R.D. College, Bairgainia, Sitamarhi – 843313,  B.R.A. Bihar University Muzaffarpur – 842001, Bihar, India. Mob. (Whatsapp) : 8757554888, Email Id : 11786mdshahabuddin@gmail.com
    3. Pandit Umashankar Mahila Mahavidyalay, Bagaha, West Champaran – 845101, B.R.A. Bihar University Muzaffarpur – 842001, Bihar, India. Mob. (Whatsapp) : 6386430281, Email Id : pramodpandey5926@gmail.com
    4. R.D.S. College, Muzaffarpur – 842002, B.R.A. Bihar University Muzaffarpur – 842001, Bihar, India. Mob. & Whatsapp No. – 7828073610
    5. R.S.S. College, Chochahan, Muzaffarpur – 844111, B.R.A. Bihar University Muzaffarpur – 842001, Bihar, India. Mob. : 9934968664 ; Whatsapp No. : 7070225503, Email Id : dr.umeshkumarsrivastava@gmail.com

    Abstract: This paper presents the study of equi – continuous spaces in linear Topological spaces. Here, we consider an order – infrabarreled Locally solid locally convex Riesz space (denoted by E) and Linear space of absolutely summable real sequence (denoted by 11), it is proved in this paper that if every compact linear operator from E to 11 is expressible as the difference of positive linear operators, then equi- continuous sets in the space of continuous linear functionals on E bounded above therein.

    Keywords: Equi – Continuous Space, Riesz Space, Locally Convex Space, Linear Operators, Compact Operators, Lattice.

    Pages: 11 – 18 | Full PDF Paper