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In mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space [1] [2]) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a scalar, often denoted with angle brackets such as in , .
A real inner product space is defined in the same way, except that H is a real vector space and the inner product takes real values. Such an inner product will be a bilinear map and ( H , H , ⋅ , ⋅ ) {\displaystyle (H,H,\langle \cdot ,\cdot \rangle )} will form a dual system .
WTVM (channel 9) is a television station in Columbus, Georgia, United States, affiliated with ABC.It is owned by Gray Television, which provides certain services to dual NBC/CW+ affiliate WLTZ (channel 38, owned by SagamoreHill Broadcasting) [2] and Fox affiliate WXTX (channel 54, owned by American Spirit Media) under separate shared services agreements (SSAs).
This article will deal with the second, called a L-semi-inner product or semi-inner product in the sense of Lumer, which is an inner product not required to be conjugate symmetric. It was formulated by Günter Lumer , for the purpose of extending Hilbert space type arguments to Banach spaces in functional analysis . [ 1 ]
WLTZ (channel 38) is a television station in Columbus, Georgia, United States, affiliated with NBC and The CW Plus.It is owned by SagamoreHill Broadcasting, which maintains a shared services agreement (SSA) with Gray Television, owner of ABC affiliate WTVM (channel 9), for the provision of certain services.
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WXTX (channel 54) is a television station in Columbus, Georgia, United States, affiliated with the Fox network. It is owned by American Spirit Media, which maintains a shared services agreement (SSA) with Gray Television, owner of ABC affiliate WTVM (channel 9), for the provision of certain services.
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