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Therefore, is a bounded operator in the space of.
It is obvious that each weighted composition operator is a bounded operator on the ball algebra.
Then the operator is a bounded operator from to.
Let be two commuting bounded operators on the Banach space.
The case of a bounded operator can be treated assuming extra conditions on the operator.
where is the bounded operator, or as (2.13).
For notational simplicity, we consider only the particular case where the nonlinearity b (u ) is a bounded operator.
Equivalently, a bounded operator T is compact if, for any bounded sequence {xk}, the sequence {Txk} has a convergent subsequence.
Then the inverse Fourier transform defines a bounded operator (3.7).
It is straightforward that the operator Γ 0 b is a linear bounded operator.
It is straightforward that the operator (Gamma_{0}^{b}) is a linear bounded operator.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com