OPERATOR ACCRETIVE KUAT PADA RUANG HILBERT

Razis Aji Saputro, Susilo Hariyanto, Y.D. Sumanto


DOI: https://doi.org/10.14710/jfma.v1i1.10

Abstract


Pre-Hilbert space is a vector space equipped with an inner-product. Furthermore, if each Cauchy sequence in a pre-Hilbert space is convergent then it can be said complete and it called as Hilbert space. The accretive operator is a linear operator in a Hilbert space. Accretive operator is occurred if the real part of the corresponding inner product will be equal to zero or positive. Accretive operators are also associated with non-negative self-adjoint operators. Thus, an accretive operator is said to be strict if there is a positive number such that the real part of the inner product will be greater than or equal to that number times to the squared norm value of any vector in the corresponding Hilbert Space. In this paper, we prove that a strict accretive operator is an accretive operator.


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References


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Berberian, Sterling. K, Introduction to Hilbert Space, New York: Oxford university Press, 1961.


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