diff --git a/Project.toml b/Project.toml
index 579daf6..fd11f26 100644
--- a/Project.toml
+++ b/Project.toml
@@ -3,5 +3,15 @@ uuid = "621c0da3-e96e-4f80-bd06-5ae31cdfcb39"
 authors = ["ITensor developers <support@itensor.org> and contributors"]
 version = "0.1.0"
 
+[deps]
+ConstructionBase = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
+DiskArrays = "3c3547ce-8d99-4f5e-a174-61eb10b00ae3"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+Serialization = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
+
 [compat]
+ConstructionBase = "1.5.8"
+DiskArrays = "0.4.12"
+LinearAlgebra = "1.10"
+Serialization = "1.10"
 julia = "1.10"
diff --git a/src/SerializedArrays.jl b/src/SerializedArrays.jl
index ea728be..b888e25 100644
--- a/src/SerializedArrays.jl
+++ b/src/SerializedArrays.jl
@@ -1,5 +1,120 @@
 module SerializedArrays
 
-# Write your package code here.
+using ConstructionBase: constructorof
+using DiskArrays: DiskArrays, AbstractDiskArray, Unchunked
+using LinearAlgebra: LinearAlgebra, mul!
+using Serialization: deserialize, serialize
+
+struct SerializedArray{T,N,A<:AbstractArray{T,N},Axes} <: AbstractDiskArray{T,N}
+  file::String
+  axes::Axes
+end
+file(a::SerializedArray) = getfield(a, :file)
+Base.axes(a::SerializedArray) = getfield(a, :axes)
+arraytype(a::SerializedArray{<:Any,<:Any,A}) where {A} = A
+
+function SerializedArray(file::String, a::AbstractArray)
+  serialize(file, a)
+  ax = axes(a)
+  return SerializedArray{eltype(a),ndims(a),typeof(a),typeof(ax)}(file, ax)
+end
+function SerializedArray(a::AbstractArray)
+  return SerializedArray(tempname(), a)
+end
+
+function Base.similar(a::SerializedArray, elt::Type, dims::Tuple{Vararg{Int}})
+  return constructorof(arraytype(a)){elt}(undef, dims...)
+end
+
+function Base.copy(a::SerializedArray)
+  arrayt = arraytype(a)
+  return convert(arrayt, deserialize(file(a)))::arrayt
+end
+
+Base.size(a::SerializedArray) = length.(axes(a))
+
+#
+# DiskArrays
+#
+
+DiskArrays.haschunks(::SerializedArray) = Unchunked()
+function DiskArrays.readblock!(
+  a::SerializedArray{<:Any,N}, aout, i::Vararg{AbstractUnitRange,N}
+) where {N}
+  if i == axes(a)
+    aout .= copy(a)
+    return a
+  end
+  aout .= @view copy(a)[i...]
+  return a
+end
+function DiskArrays.writeblock!(
+  a::SerializedArray{<:Any,N}, ain, i::Vararg{AbstractUnitRange,N}
+) where {N}
+  if i == axes(a)
+    serialize(file(a), ain)
+    return a
+  end
+  a′ = copy(a)
+  a′[i...] = ain
+  serialize(file(a), a′)
+  return a
+end
+function DiskArrays.create_outputarray(::Nothing, a::SerializedArray, output_size::Tuple)
+  return similar(a, output_size)
+end
+
+#
+# Broadcast
+#
+
+using Base.Broadcast:
+  BroadcastStyle, Broadcasted, DefaultArrayStyle, combine_styles, flatten
+
+struct SerializedArrayStyle{N} <: Base.Broadcast.AbstractArrayStyle{N} end
+Base.BroadcastStyle(arrayt::Type{<:SerializedArray}) = SerializedArrayStyle{ndims(arrayt)}()
+function Base.BroadcastStyle(
+  ::SerializedArrayStyle{N}, ::SerializedArrayStyle{M}
+) where {N,M}
+  SerializedArrayStyle{max(N, M)}()
+end
+function Base.BroadcastStyle(::SerializedArrayStyle{N}, ::DefaultArrayStyle{M}) where {N,M}
+  return SerializedArrayStyle{max(N, M)}()
+end
+function Base.BroadcastStyle(::DefaultArrayStyle{M}, ::SerializedArrayStyle{N}) where {N,M}
+  return SerializedArrayStyle{max(N, M)}()
+end
+
+struct BroadcastSerializedArray{T,N,BC<:Broadcasted{<:SerializedArrayStyle{N}}} <:
+       AbstractDiskArray{T,N}
+  broadcasted::BC
+end
+function BroadcastSerializedArray(
+  broadcasted::B
+) where {B<:Broadcasted{<:SerializedArrayStyle{N}}} where {N}
+  ElType = Base.Broadcast.combine_eltypes(broadcasted.f, broadcasted.args)
+  return BroadcastSerializedArray{ElType,N,B}(broadcasted)
+end
+Base.size(a::BroadcastSerializedArray) = size(a.broadcasted)
+Base.broadcastable(a::BroadcastSerializedArray) = a.broadcasted
+function Base.copy(a::BroadcastSerializedArray)
+  # Broadcast over the materialized arrays.
+  return copy(Base.Broadcast.broadcasted(a.broadcasted.f, copy.(a.broadcasted.args)...))
+end
+
+function Base.copy(broadcasted::Broadcasted{SerializedArrayStyle{N}}) where {N}
+  return BroadcastSerializedArray(flatten(broadcasted))
+end
+
+#
+# LinearAlgebra
+#
+
+function LinearAlgebra.mul!(
+  a_dest::AbstractMatrix, a1::SerializedArray, a2::SerializedArray, α::Number, β::Number
+)
+  mul!(a_dest, copy(a1), copy(a2), α, β)
+  return a_dest
+end
 
 end
diff --git a/test/Project.toml b/test/Project.toml
index 3309f69..3064946 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -1,13 +1,21 @@
 [deps]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527"
+JLArrays = "27aeb0d3-9eb9-45fb-866b-73c2ecf80fcb"
 SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 SerializedArrays = "621c0da3-e96e-4f80-bd06-5ae31cdfcb39"
+StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 Suppressor = "fd094767-a336-5f1f-9728-57cf17d0bbfb"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+TestExtras = "5ed8adda-3752-4e41-b88a-e8b09835ee3a"
 
 [compat]
-Aqua = "0.8.9"
+Aqua = "0.8"
+GPUArraysCore = "0.2"
+JLArrays = "0.2"
 SafeTestsets = "0.1"
 SerializedArrays = "0.1"
+StableRNGs = "1"
 Suppressor = "0.2"
 Test = "1.10"
+TestExtras = "0.3"
diff --git a/test/test_basics.jl b/test/test_basics.jl
index 808728b..5bc6690 100644
--- a/test/test_basics.jl
+++ b/test/test_basics.jl
@@ -1,6 +1,39 @@
-using SerializedArrays: SerializedArrays
+using GPUArraysCore: @allowscalar
+using JLArrays: JLArray
+using SerializedArrays: SerializedArray
+using StableRNGs: StableRNG
 using Test: @test, @testset
+using TestExtras: @constinferred
 
-@testset "SerializedArrays" begin
-  # Tests go here.
+elts = (Float32, Float64, Complex{Float32}, Complex{Float64})
+arrayts = (Array, JLArray)
+@testset "SerializedArrays (eltype=$elt, arraytype=$arrayt)" for elt in elts,
+  arrayt in arrayts
+
+  rng = StableRNG(123)
+  x = arrayt(randn(rng, elt, 4, 4))
+  a = SerializedArray(x)
+  @test @constinferred(copy(a)) == x
+  @test typeof(copy(a)) == typeof(x)
+
+  x = arrayt(zeros(elt, 4, 4))
+  a = SerializedArray(x)
+  @allowscalar begin
+    a[1, 1] = 2
+    @test @constinferred(a[1, 1]) == 2
+  end
+
+  x = arrayt(zeros(elt, 4, 4))
+  a = SerializedArray(x)
+  b = 2a
+  @test @constinferred(copy(b)) == 2x
+
+  rng = StableRNG(123)
+  x = arrayt(randn(rng, elt, 4, 4))
+  y = arrayt(randn(rng, elt, 4, 4))
+  a = SerializedArray(x)
+  b = SerializedArray(y)
+  c = @constinferred(a * b)
+  @test c == x * y
+  @test c isa arrayt{elt,2}
 end