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Bill Johnson
Bill Johnson
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See

[11] Ruess, W.M. and Stegall, C.P., Extreme points in duals of operator spaces, Math. Ann., 261 (1982), 535–546.

They prove what you want in a more general context: If $X$, $Y$ are Banach spaces s.t. either $X^*$ or $Y^*$ has the approximation property and either $X^*$ or $Y^*$ has the Radon-Nikodyn property, then the extreme points of the unit ball of the projective tensor product of $X^*$ and $Y^*$ are the tensor products of extreme points of the respective unit balls.

See

[11] Ruess, W.M. and Stegall, C.P., Extreme points in duals of operator spaces, Math. Ann., 261 (1982), 535–546.

They prove what you want in a more general context: If $X$, $Y$ are Banach spaces s.t. either $X^*$ or $Y^*$ has the approximation property and either $X^*$ or $Y^*$ has the Radon-Nikodyn property, then the extreme points of the unit ball of the projective tensor product of $X^*$ and $Y^*$ are the tensor products of extreme points of the respective unit balls.

See

[11] Ruess, W.M. and Stegall, C.P., Extreme points in duals of operator spaces, Math. Ann., 261 (1982), 535–546.

They prove what you want in a more general context: If $X$, $Y$ are Banach spaces s.t. either $X^*$ or $Y^*$ has the approximation property and either $X^*$ or $Y^*$ has the Radon-Nikodyn property, then the extreme points of the unit ball of the projective tensor product of $X^*$ and $Y^*$ are the tensor products of extreme points of the respective unit balls.

Source Link
Bill Johnson
Bill Johnson
  • 31.5k
  • 5
  • 90
  • 138

See

[11] Ruess, W.M. and Stegall, C.P., Extreme points in duals of operator spaces, Math. Ann., 261 (1982), 535–546.

They prove what you want in a more general context: If $X$, $Y$ are Banach spaces s.t. either $X^*$ or $Y^*$ has the approximation property and either $X^*$ or $Y^*$ has the Radon-Nikodyn property, then the extreme points of the unit ball of the projective tensor product of $X^*$ and $Y^*$ are the tensor products of extreme points of the respective unit balls.