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MMLU-Pro / 8424 / Suppose H is a Banach space. Let A be a linear functional on the space H that…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Suppose H is a Banach space. Let A be a linear functional on the space H that maps H to H. Suppose operator A satisfies: for all x∈Hx\in H, ||Ax||≥a||x||||Ax||\geq a ||x|| for some a>0. If A is not a compact operator on H, Is the dimension of H finite or infinite? Return 1 for finite dimension and 0 for infinite dimension
Plain-text mathematical notation (without MathML)
Suppose H is a Banach space. Let A be a linear functional on the space H that maps H to H. Suppose operator A satisfies: for all x∈H, ||Ax||≥a||x|| for some a>0. If A is not a compact operator on H, Is the dimension of H finite or infinite? Return 1 for finite dimension and 0 for infinite dimension
Original LaTeX notation
Suppose H is a Banach space. Let A be a linear functional on the space H that maps H to H. Suppose operator A satisfies: for all $x\in H$, $||Ax||\geq a ||x||$ for some a>0. If A is not a compact operator on H, Is the dimension of H finite or infinite? Return 1 for finite dimension and 0 for infinite dimension

category

math

options

  1. 6.0
  2. 0.0
  3. 2.0
  4. 4.0
  5. 9.0
  6. 8.0
  7. 5.0
  8. 3.0
  9. 7.0
  10. 1.0

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8424
task_id
e289dbb8-d3a4-543d-9552-cfe98af57607
task_key
default--test--8424
task_revision_id
1
config / split
default / test

Official source

initial import