In Volume 4 of Reed and Simon on page 83 the authors refer to the space $(L^\infty(\mathbb{R}^3))_\varepsilon$,

and later on page 119 they use $L^\\infty_\varepsilon$. Are these two spaces the same? Is that the set of functions $f$ such that $(1+|x|^2)^{\varepsilon/2} f \in L^\infty$?

Thanks for any help -- I really tried looking this up for a while and turned up nothing, and it didn't seem to be in the index!

In Volume 4 of Reed and Simon on page 83 the authors refer to the space $(L^\infty(\mathbb{R}^3))_\varepsilon$,

and later on page 119 they use $L^\\infty_\varepsilon$. Are these two spaces the same? Is that the set of functions $f$ such that $(1+|x|^2)^{\varepsilon/2} f \in L^\infty$?

Thanks for any help -- I really tried looking this up for a while and turned up nothing, and it didn't seem to be in the index!

PS Just to motivate the question, Theorem XIII.15 of that book says (among other things), that if $V \in L^\infty_\varepsilon$, then the essential spectrum of $-\Delta + V$ is $[0,\infty)$.

In Volume 4 of Reed and Simon on page 83 the authors refer to the space $(L^\infty(\mathbb{R}^3))_\varepsilon$,

and later on page 119 they use $L^\\infty_\varepsilon$. Are these two spaces the same? Is that the set of functions $f$ such that $(1+x^2)^{\varepsilon/2} f \in L^\infty$?

Thanks for any help -- I really tried looking this up for a while and turned up nothing, and it didn't seem to be in the index!

In Volume 4 of Reed and Simon on page 83 the authors refer to the space $(L^\infty(\mathbb{R}^3))_\varepsilon$,

and later on page 119 they use $L^\\infty_\varepsilon$. Are these two spaces the same? Is that the set of functions $f$ such that $(1+|x|^2)^{\varepsilon/2} f \in L^\infty$?

Thanks for any help -- I really tried looking this up for a while and turned up nothing, and it didn't seem to be in the index!