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I read an article, it contains sentence like this - The hilbert space A possesses the bounded point evaluation property. What does this mean? I found this Meaning of Point Evaluation, is it connected with that property?

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aptypr
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It means that the Hilbert space $A$ consists of functions $f$ defined on some set $X$, and for every point $x\in X$ the linear functional $f\mapsto f(x)$ is bounded on $A$. Such spaces are also known as reproducing kernel Hilbert spaces.

Remark. Because the meaning of mathematical terms may depend on the context in which they are used, in general you will get a more precise answer by providing a reference to the source.

  • I am satisfied with this answer. The source is article "Riesz bases of reproducing kernels in fock type spaces" be Borichev and Lyubarskii. – aptypr Apr 20 '13 at 10:18