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INTERNATIONAL JOURNAL OF SCIENTIFIC DEVELOPMENT AND RESEARCH
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ISSN Approved Journal No: 2455-2631 | Impact factor: 8.15 | ESTD Year: 2016
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Paper Title:	Mutually Singular Measurable Subspaces of a Linear Space
Authors Name:	T Srinivasarao , Dr. L.Sujatha
Unique Id:	IJSDR2207090
Published In:	Volume 7 Issue 7, July-2022
Abstract:	A linear space can be made a measurable space’. By taking subsets of the linear space and their linear spans as the elements of ℬ. This work is an exercise to bring out the relationship between the subspaces of a linear space and the respective dimensions as measures that follows the properties of subspaces with respect to the dimension of a subspace or equivalently with respect to the measure. Orthogonal complements in the case of subspaces will be seen as mutually singular measurable subspaces. So, the direct sum of a subspace and its orthogonal complement will be the direct sum of the mutually singular measurable subspaces of a measurable space
Keywords:	The linear span of a subset S of a linear space U(F) is L(S) L(S) is a subspace of a linear space L(S_1)⊕L(S_2) is the direct sum of subspaces B_S is the standard basis of the linear space R(T) is the range of T and P(R(T)) is the inverse image of R(T) in U(F) 〖(L(P(R(T)) ))〗^t is the transpose of the subspace µ (L(S)) = dim L(S): the dimension of the linear space is the measure μ
Cite Article:	"Mutually Singular Measurable Subspaces of a Linear Space", International Journal of Science & Engineering Development Research (www.ijsdr.org), ISSN:2455-2631, Vol.7, Issue 7, page no.610 - 611, July-2022, Available :http://www.ijsdr.org/papers/IJSDR2207090.pdf
Downloads:	000337074
Publication Details:	Published Paper ID: IJSDR2207090 Registration ID:201043 Published In: Volume 7 Issue 7, July-2022 DOI (Digital Object Identifier): Page No: 610 - 611 Publisher: IJSDR \| www.ijsdr.org ISSN Number: 2455-2631

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