approximation property造句

• A Banach space with a Schauder basis is necessarily bounded approximation property.
• This deep architecture allows the design of neural networks with universal approximation properties.
• On the other hand, Szankowski proved that the classical space does not have the approximation property.
• Grothendieck's work on the theory of Banach spaces and continuous linear operators introduced the approximation property.
• Grothendieck thus focused the attention of functional analysts on deciding whether every Banach space have the approximation property.
• The space of bounded operators on \ ell ^ 2 does not have the approximation property ( Szankowski ).
• A Banach space is said to have the approximation property, if every compact operator is a limit of finite-rank operators.
• :* X has the ( classical ) approximation property \ Longleftrightarrow X ^ \ star has the ( classical ) approximation property;
• :* X has the ( classical ) approximation property \ Longleftrightarrow X ^ \ star has the ( classical ) approximation property;
• This was negatively answered by Per Enflo who constructed a separable Banach space failing the approximation property, thus a space without a Schauder basis.
• Furthermore, just as Enflo's example, this space is a " hand-made " space that fails to have the approximation property.
• In a long monograph, Grothendieck proved that if every Banach space had the approximation property, then every Banach space would have a Schauder basis.
• Weak approximation holds for a broader class of groups, including adjoint groups and inner forms of Chevalley groups, showing that the strong approximation property is restrictive.
• The spaces \ ell ^ p for p \ neq 2 and c _ 0 ( see Sequence space ) have closed subspaces that do not have the approximation property.
• Whether this was true in general for Banach spaces ( the approximation property ) was an unsolved question for many years; in the end Per Enflo gave a counter-example.
• In particular, if X has the stereotype approximation property, then the same is true for X ^ \ star and for \ text { Hom } ( X, X ).
• The key approximation property used to construct these filters is that the data dependent covariance ( unlike the Gaussian case ) this derivation also provides one of the nicest ways of establishing the standard Kalman filter recursions.
• This condition is weaker than the existence of the Schauder basis, but formally stronger than the classical approximation property ( however, it is not clear ( 2013 ) whether the stereotype approximation property coincide with the classical one, or not ).
• This condition is weaker than the existence of the Schauder basis, but formally stronger than the classical approximation property ( however, it is not clear ( 2013 ) whether the stereotype approximation property coincide with the classical one, or not ).
• :* If two stereotype spaces X and Y have the stereotype approximation property, then the spaces \ text { Hom } ( X, Y ), X \ circledast Y and X \ odot Y have the stereotype approximation property as well.