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edit approved Feb 19, 2018 at 20:59
Alex M.
edit approved Feb 19, 2018 at 20:59
Alex M.
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in embry'sIn Embry's 1973 and douglas'Douglas' 1966 papers the hilbertHilbert space condition AA* < lambda^2 BB*$AA^* < \lambda^2 BB^*$ about the adjoints is replaced by the following equivalent banachBanach type of condition: ||A|| < lambda ||B||$\|A\| < \lambda \|B\|$, so that the whole exotic question of banachBanach space adjoints A*:X-->X$A^* : X \to X$ analogous to hilbertHilbert space adjoints is avoided.

onOn the other hand, if A:X-->Y$A:X \to Y$, the banachBanach space adjoint defined as A*:Y-->X using$A^* : Y^* \to X^*$ using duality theory does play an important role in the results of douglasDouglas and embryEmbry. embry'sEmbry's is accessible on the free internet and is easy to read.

in embry's 1973 and douglas' 1966 papers the hilbert space condition AA* < lambda^2 BB* about the adjoints is replaced by the following equivalent banach type of condition: ||A|| < lambda ||B||, so that the whole exotic question of banach space adjoints A*:X-->X analogous to hilbert space adjoints is avoided.

on the other hand, if A:X-->Y the banach space adjoint defined as A*:Y-->X using duality theory does play an important role in the results of douglas and embry. embry's is accessible on the free internet and is easy to read.

In Embry's 1973 and Douglas' 1966 papers the Hilbert space condition $AA^* < \lambda^2 BB^*$ about the adjoints is replaced by the following equivalent Banach type of condition: $\|A\| < \lambda \|B\|$, so that the whole exotic question of Banach space adjoints $A^* : X \to X$ analogous to Hilbert space adjoints is avoided.

On the other hand, if $A:X \to Y$, the Banach space adjoint defined as $A^* : Y^* \to X^*$ using duality theory does play an important role in the results of Douglas and Embry. Embry's is accessible on the free internet and is easy to read.

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nir cohen
nir cohen
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in embry's 1973 and douglas' 1966 papers the hilbert space condition AA* < lambda^2 BB* about the adjoints is replaced by the following equivalent banach type of condition: ||A|| < lambda ||B||, so that the whole exotic question of banach space adjoints A*:X-->X analogous to hilbert space adjoints is avoided.

on the other hand, if A:X-->Y the banach space adjoint defined as A*:Y-->X using duality theory does play an important role in the results of douglas and embry. embry's is accessible on the free internet and is easy to read.