1. Weak Linear Independence of Vector Spaces

    Hamza Hakmi1, Eaman Al-Khouja2, Adnan Al-Taybani2

    1. Department of Mathematics, Faculty of Sciences, Damascus University, Damascus, Syria.
    2. Department of Mathematics, Faculty of Sciences, Al-Baath University, Homs, Syria.

    Abstract: 

    The problem of generation and oneness considered for expressing about an element is very important and has a big effect in mathematics in general and in algebra in special for example in vector spaces, every element from this space is expressed in a unique way as a linear combination of elements of its base.
    In this paper, we introduce and study new concepts in vector space over a field, to express every element from this space in a unique way called weak linear combination.

    Keywords: Weak linear combination, Weak generation, Weak linear independence, Full linear dependence, Weak base, Independent weak base.

    Pages: 157 – 181 | Full PDF Paper

  2. Analytical Study of Hilbert Space and Algebra of Operators

    U.K. Srivastava1, L.K. Roy2, Binod Prasad3, C.D. Pathak4, & Surendra Ray5

    1. R.S.S. College, Chochahan, P.O.:- Aniruddh Belsar, Dist.- Muzaffarpur – 844111, B.R.A. Bihar University, Muzaffarpur – 842001,
    Bihar, India    .
    2. T.P. Varma College, Narkatiaganj, West Champaran – 845455 , B.R.A. Bihar University, Muzaffarpur – 842001 , Bihar, India.
    3. T.R.M. Campus, Birganj, Parsa, Nepal, Tribhuvan University, Nepal.
    4. R.R.M. Campus, Janakpurdham, Nepal, Tribhuvan University, Nepal.
    5. R.R.M. Campus, Janakpurdham, Nepal, Tribhuvan University, Nepal.

    Abstract:     This present paper deals with the study of Hilbert Space and Algebra of Operators. Here, we consider R as additive group of reals with discrete topology and several ways of constructing C* – algebras Canonically associated with R and π, The Universal representation of R on Hilbert Space H, it is proved in this paper that all C*- algebras homomorphism and representation will be * – preserving.

    Keywords:     Hilbert space, Tensor product, C* – tensor norms, C* – algebras, Normal and Binormal norms, W*- algebras.

    Pages: 182 – 186 | Full PDF Paper